How Things Work - Chapter 3 Demonstrations
Section 3.1 Spring Scales
Demonstration 3.1.1: "Measuring" Mass by Shaking
Description: A massive object is found inside two identical containers by shaking them to "measure" the masses of those containers.
Purpose: To illustrate that you can quantify "how much" there is of an object by measuring its mass
2 identical low-mass containers, each hanging from a cord.
1 massive object, to hide in one of the containers.
Procedure: Have a student close his/her eyes while you hide the massive object in one of the containers. Then have the student find the object without lifting either container (weighing is forbidden). Of course, the student will shake the two containers and easily discover which one is the more massive and thus which one contains the object.
Explanation: Shaking the container measures its mass. The more massive it is, the less it will accelerate in response to a given force.
Demonstration 3.1.2: "Measuring" Weight by Lifting
Description: A heavy object is found inside two identical containers by lifting them to "measure" the weights of those containers.
Purpose: To illustrate that you can quantify "how much" there is of an object by measuring its weight
2 identical low-weight containers, each hanging from a cord.
1 heavy object, to hide in one of the containers.
Procedure: Have a student close his/her eyes while you hide the heavy object in one of the containers. Then have the student find the object without shaking either container (measuring mass is forbidden). Of course, the student will slowly lift the two containers and easily discover which one is heavier and thus which one contains the object.
Explanation: Lifting the container measures its weight. The heavier it is, the more upward force the student will have to exert on it to support its weight so that it doesn't accelerate.
Demonstration 3.1.3: An Object Hanging in Equilibrium
Description: The heavy object from the previous demonstrations simply hangs at equilibrium, its weight supported perfectly by the upward pull of a cord.
Purpose: To illustrate equilibrium.
1 heavy object, hanging from a cord.
Procedure: Hang the heavy object and let everything settle so that nothing is accelerating. Ask whether the object has lost its weight. Ask why the object isn't falling. Ask how hard the cord must be pulling up on the object and have someone explain that answer. Ask what question you might pose to the cord that would allow you to determine the object's weight. Discuss also whether the object must be motionless for this procedure to work, or whether they must merely be at constant velocity. If you're ambitious, you could carry the hanging object steadily across the room (at constant velocity) to illustrate that equilibrium means zero acceleration, not (necessarily) zero velocity.
Explanation: The cord is supporting the object's weight: it is exerting an upward force on the object that's equal in amount to the object's weight, but in the upward direction. The object is thus in equilibrium, which is why it doesn't fall. If you could get the cord to tell you how hard it is pulling upward on the object, you'd know the weight of the object.
Demonstration 3.1.4: A Spring's Behavior At and Near Equilibrium
Description: A coil spring, supported from above, is shown to exert a restoring force that's proportional to how far it's distorted away from its equilibrium shape or position.
Purpose: To illustrate equilibrium and to show that a spring's restoring forces are proportional to its distortion (Hooke's law).
1 coil spring
1 support for the coil spring (supporting it from above)
1 ruler or other measuring device (it should be fixed in place next to the coil spring so that the students can see how the spring's length changes)
3 or more identical reference weights
Procedure: Suspend the coil spring from the support and align the ruler next to it so that the ruler's zero is next to the spring's free end. Point out that the end of the spring is motionless and not accelerating, so that it must be experiencing a net force of zero—it must be in equilibrium. Now hang first one, then two, then all three reference weights from the spring. Note that the spring adopts a new equilibrium height after each addition. Since the weights' weights are being exerted downward on the spring, the spring must be pulling upward on the weights with a force that's equal in magnitude to their weights. Point out that the spring has had to stretch in order to exert this upward force on the weights and that the extent of this stretch is proportional to the upward force the spring is exerting on the weights. Determine the distance stretch per unit of force exerted, thereby calibrating the spring.
Explanation: The spring obeys Hooke's law, exerting an upward force on the objects that's proportional to how far the spring has been stretched downward. Since two objects weigh twice as much as a single object, the spring must stretch twice as far. For three objects, it must stretch three times as far.
Demonstration 3.1.5: A Ruler is a Spring
Description: A flexible ruler that extends from the edge of a table acts as a spring when objects are placed on it.
Purpose: To show that almost everything acts as a spring when deformed slightly.
1 flexible ruler (a plastic ruler or a wooden meter stick)
3 identical objects
1 heavy book (or any other anchor for the ruler)
Procedure: Extend the ruler from the edge of a table, using the book to anchor its supported end to the table. Note that the free end of the ruler adopts an equilibrium height. Now add first one, then two, then three objects to the end of the ruler. Point out that the ruler deforms downward with each additional object and that the amount of its deformation is proportional to the weight that it's supporting.
Explanation: The ruler is acting as a spring, deforming downward by an amount that's proportional to the restoring force it's experiencing. This restoring force is supporting the weight of the objects on its end. Since the objects have equal weights, the ruler's restoring force and its deformation are both proportional to the number of objects the ruler is supporting.
Demonstration 3.1.6: Weigh An Object Hanging in Equilibrium Using the Spring
Description:The heavy object from the previous demonstrations is hung from the spring at equilibrium, and its weight is measured by observing the spring's distortion.
Purpose: To show how a spring scale measures weight.
1 heavy object
1 coil spring
1 support for the coil spring (supporting it from above)
1 ruler or other measuring device (it should be fixed in place next to the coil spring so that the students can see how the spring's length changes)
Procedure: Let the spring settle at equilibrium. Note the current position of the spring's unsupported end. Now hang the heavy object from the spring and again let the system settle at equilibrium. Note the new position of the spring's unsupported end. Using the calibration of the spring from the previous demonstrations, determine how much the object weighs. Ask why it's important to not touch the object during weighing. Ask why it's important that the object not be accelerating during weighing.
Explanation: The spring is now supporting the weight of the object, so it is exerting an upward force on the object equal in magnitude to the object's weight. The spring is using its restoring force to exert that upward force, so it is distorted by an amount that is proportional to the object's weight. Having calibrated the spring (its restoring force per unit of distortion), it's now possible to measure the object's weight.
Demonstration 3.1.7: A Hanging Spring Scale
Description: As you hang an object from a hanging spring scale, it's spring stretches and its needle indicates the object's weight.
Purpose: To show that a hanging scale is a spring scale.
1 hanging spring scale
1 weight to hang from it
Procedure: Hang the weight from the spring scale and watch the spring stretch and the needle move. Show that the needle is actually reporting the spring's stretch, calibrated so that it appears in units of weight. Show the importance of waiting until nothing is accelerating.
Explanation: The hanging scale contains a spring that deforms as you add weights to the scale. This deformation allows the spring to exert the upward support force that keeps the weights from falling. The scale's hanger descends until the spring's restoring force is just enough to provide an upward support force that's equal in magnitude to the weights of the objects the scale is supporting.
Demonstration 3.1.8: A Pan Spring Scale
Description: As you place an object on a pan spring scale, it's spring stretches and its needle indicates the object's weight.
Purpose: To show that a pan scale is a spring scale.
1 pan spring scale
1 weight to place on it
Procedure: Place the weight on the spring scale and watch the spring stretch and the needle move. Show that the needle is actually reporting the spring's stretch, calibrated so that it appears in units of weight. Show the importance of waiting until nothing is accelerating.
Explanation: The pan scale contains a spring that deforms as you add weights to the scale. This deformation allows the spring to exert the upward support force that keeps the weights from falling. The scale's pan descends until the spring's restoring force is just enough to provide an upward support force that's equal in magnitude to the weights of the objects the scale is supporting.
Demonstration 3.1.9: A Bathroom Scale
Description: As you step on a bathroom scale, its surface descends slightly as the spring inside it deforms. The scale measures this deformation in order to determine your weight.
Purpose: To show that even a bathroom scale is really a spring scale.
1 bathroom scale
Procedure: Step on a bathroom scale and watch the scale's surface descend. Show that the more weight you place on this scale, the farther downward the scale's surface goes. Pick up the scale and squeeze it to show the direct relationship between how far inward you push its surface and the weight that it reports on its dial.
Explanation: The bathroom scale contains a spring that deforms as you step on the scale. This deformation allows the spring to exert the upward support force that keeps you from falling into the scale's surface. The scale's surface descends until the spring's restoring force is just enough to provide its surface with an upward support force that's equal in magnitude to your weight.
Demonstration 3.1.10: Jumping on a Bathroom Scale
Description: As you jump on a bathroom scale, it reads heavy and then light.
Purpose: To show that a bathroom scale reports the force it exerts on you, not necessarily your weight.
1 bathroom scale
Procedure: Step on a bathroom scale and, after letting it settle to equilibrium, observe the scale's reading -- your weight. Now jump upward and watch as the scale reads more than your weight, then less than your weight. Ask what the scale is reporting. Ask if your weight changed during that experiment. Ask why it's so important that you not jump during weighing.
Explanation: The bathroom scale reports the force that it exerts on you. If you're not accelerating, then that force is equal in magnitude to your weight. But if you're jumping upward and accelerating upward, then the upward force that the scale exerts on you is greater in magnitude than your weight. And as you subsequently fall, the scale exerts less force on you than the magnitude of your weight.
Demonstration 3.1.11: An Accelerating Spring Scale
Description: An object hangs from a spring scale as both bounce slowly up and down on the end of a very long spring. The spring scale reads alternately more or less than the object's actual weight.
Purpose: To show that when a scale and the object it's supporting accelerate, the force that the scale exerts on the object isn't equal in magnitude to the object's weight.
1 spring scale
1 very long spring or elastic cord
Procedure: Suspend the object from the spring scale and then suspend the spring scale from the very long spring. Allow the scale to hang motionless from the spring and note that the scale reads the true weight of the object. Then make the scale and object bounce gently up and down. The scale will alternately read more or less than the object's weight.
Explanation: Whenever the scale and object are below their equilibrium position and the very long spring is stretched downward, the scale and object are accelerating upward. The scale must therefore pull upward extra hard on the object and the scale reads more than the object's weight. Whenever the scale and object are above their equilibrium position, they are accelerating downward and the scale reads less than the object's weight.
Follow-up: Allow the scale and object to bounce so high that they enter free fall. At that point, the scale will read zero! Be careful that the object doesn't fall off the spring scale.
Demonstration 3.1.12: A Hanging Pan Centers Itself Automatically
Description: A hanging pan automatically adjusts its angle so that its center of gravity is directly below its support.
Purpose: To show that a hanging object will tip until its center of gravity is directly below the point from which it's being supported.
1 hanging pan (or any basket that's supported by strings that merge to a single point of support)
1 support for the pan
3 objects to put in the pan
Procedure: Suspend the hanging pan from the support and allow it to settle. Its center of gravity should then be directly below the point from which it's supported. Now begin adding the objects to the pan. Show that the pan tips until its new center of gravity is directly below the support point.
Explanation: When the pan's center of gravity is directly below its support point, the pan is in equilibrium—it experiences no net force and no net torque. But whenever the pan's center of gravity isn't below the support point, it experiences a torque about its support point that restores it to its equilibrium position. This torque is a restoring torque because, just as restoring force of a spring returns it to its equilibrium position, this restoring torque always returns the pan to its equilibrium orientation.
Demonstration 3.1.13: The Difficulty in Weighing an Astronaut
Description: You jump off a stool while holding a loaded spring scale. The scale reads zero while you are falling.
Purpose: To show that a spring scale only reads the weight of the objects its holding when the objects aren't accelerating.
1 spring scale
1 short stool
Procedure: Hang the object from the spring scale and stand motionless on the stool. The scale will read the weight of the object. Now jump carefully from the stool and allow the scale and the object to fall with you. Pay attention to your landing so that you don't hurt yourself. During the time that you, the scale, and the object are in free fall, the scale will read zero.
Explanation: When the object is falling, the only force acting on it is gravity. Since the scale doesn't exert any upward force on the object, the scale's spring doesn't distort and the scale reports that it's exerting zero force on the object.
Section 3.2 Bouncing Balls
Demonstration 3.2.1: How Different Balls Bounce
Description: Several different balls rebound to different heights after being dropped.
Purpose: To show that different balls have different coefficients of restitution and thus return different fractions of the collision energy as rebound energy.
3 different balls (or more)
1 set of happy and unhappy balls (optional—available from a scientific supply company)
Procedure: Drop the different balls one at a time from a set height. Show that, while none of them return to their original heights, some bounce higher than others. Discuss how energy changes form from gravitational potential energy, to kinetic energy, to elastic potential energy (in the ball), to kinetic energy, and back to gravitational potential energy as the ball bounces. If you can obtain a happy/unhappy ball pair, show how well the happy ball bounces (essentially a superball) and how incredibly poorly the unhappy ball bounces (a remarkably dead ball—it barely bounces at all).
Explanation: As they deform during a collision, different balls have different efficiencies at storing energy. Hard balls that store energy via compression tend to bounce much better than soft balls that store energy via bending surfaces.
Demonstration 3.2.2: Bouncing from a Trampoline
Description: A relatively dead ball bounces nicely from a tightly inflated plastic bag.
Purpose: To show that the surface from which a ball bounces can contribute to the rebound.
1 non-lively ball (an "unhappy" ball is ideal and so is a beanbag)
1 air-filled plastic bag
Procedure: Show that the ball doesn't bounce well from a solid surface. Then show that the ball bounces reasonably well from the surface of the plastic bag.
Explanation: During the collision between ball and surface, the one that deforms the most receives the majority of the collision energy. Since a non-lively ball doesn't return much of the collision energy, its rebound depends critically on how lively the surface it strikes is and on what fraction of the collision energy goes into that surface. Since the plastic bag deforms easily and stores energy well, it allows even an "unhappy" ball to bounce well. While the ball returns no rebound energy, the surface does.
Demonstration 3.2.3: Bouncing from Rising Surface or Bat
Description: A baseball bounces especially high from a rising board or bat.
Purpose: To show that the movement of a surface from which a ball bounces can contribute to the rebound.
1 thick board or baseball bat
Procedure: Let baseball fall and bounce from the non-moving board (or bat) and watch how high it rebounds. Now let the baseball bounce from the board as that board is rising rapidly upward. The ball will rebound much higher. Discuss the approach speed between the ball and board in the two cases. Discuss the separation speeds in those cases. Ask where the extra energy comes from to propel the ball so high. Can you see that energy flow into the ball by way of work?
Explanation: When the ball rebounds from the stationary board, the ball's approach speed is simply its own speed. But when the board is rising to meet the falling ball, the approach speed is much greater. The separation speed is a constant fraction of the approach speed, so when the board and ball are both moving toward one another before the impact, their separation speed after the impact is that much greater. And because the ball is separating from an upward moving board, it has to move upward especially fast. In short, everything about the impact between the rising board and falling ball acts to toss the rebounding ball upward especially fast.
Demonstration 3.2.4: Ball Bouncing from a Moving Baseball Bat
Description: A human "animation" of a ball bouncing from a moving bat.
Purpose: To show the importance of inertial reference frame in following a collision between moving objects and to show how a baseball can rebound from a moving bat with a greater speed than it had before it hit the bat.
1 baseball bat
Procedure: Walk the students carefully through a collision between a ball moving at 100 km/h toward home plate and a bat moving at 100 km/h toward the pitcher. Start in the spectators' reference frame with the baseball and bat moving toward one another. Point out that the closing speed between the two is 200 km/h. Then shift to the bat's frame of reference, in which the bat is stationary, the pitcher (and the whole stadium) is heading toward home plate at 100 km/h, and the ball is heading toward home plate at 200 km/h. Allow the ball to bounce from the stationary bat (assume infinite mass for the bat) and rebound at 110 km/h (assume a coefficient of restitution of 0.55). Now the ball is heading toward the pitcher at 110 km/h from the bat's frame of reference. Finally, shift back to the spectators' frame of reference. The pitcher is stationary again and the bat is now heading toward pitcher at 100 km/h, so the ball must be heading toward the pitcher at a speed of 210 km/h (110 km/h + 100 km/h). The ball is now moving faster than anything else in the stadium!
Explanation: The collision appears simple only in the inertial frame of reference of the bat. In the spectators' frame of reference, the ball and bat are both moving when they collide and the result is somewhat counterintuitive.
Demonstration 3.2.5: A Tennis Ball Bouncing from a Basketball
Description: A tennis ball sits atop a basketball as the two are dropped from a modest height. When they hit the floor, the tennis ball leaps into the air and rises well above its original height.
Purpose: To show that bouncing from a moving surface can lead to counterintuitive results and to show the importance of picking a good inertial frame of reference from which to observe a bounce.
1 tennis ball (or another small, elastic ball)
1 basketball (or another massive, elastic ball)
Procedure: Balance the tennis ball atop the basketball and hold them a few feet above the floor or a firm table. Now drop the pair. The tennis ball should rebound to a height much greater than its original height.
Explanation: The tennis ball effectively completes its bounce from the basketball after the basketball has already bounced off the floor. As a result, the tennis ball is bouncing from a rising surface. Like a ball that's been hit by a rising baseball bat, the tennis ball rebounds with a speed that's larger than its speed before it hit the basketball. If both balls were ideally elastic (coefficients of restitution of 1.0) and if the basketball were infinitely massive, the tennis ball would rebound to 9 times its original height.
Demonstration 3.2.6: A Bouncy Ball Transfers More Momentum
Description: A bouncy object swings into a block that's balanced on its end and the block falls over. A less bouncy object of identical mass swings into the block but this time the block doesn't fall over.
Purpose: To show that a bouncy object transfers momentum during a collision both as the object slows to a stop and as it rebounds backward. An object that doesn't bounce transfers momentum only as it slows to a stop and thus transfers less momentum.
1 hard block that can be balanced on its end
1 bouncy ball (such as a happy ball)
1 non-bouncy ball (such as an unhappy ball)
1 support for balls
Procedure: Use the string to suspend the two balls from the support. Place the block on end in front of the bouncy ball, pull the ball back, and let it swing into the block. Determine how far back you must pull the ball in order to knock the block over. Now try the same experiment with the non-bouncy ball. You should have to pull it back much farther in order to knock over the block.
Alternative Procedure: Use a metal rod as a battering ram—suspend it on several strings so that it swings forward smoothly and strikes the block. Now put Silly Putty on the block to create a bouncy surface for the metal rod to hit. Determine how far back you must pull the battering ram in order to knock over the block. Now try the same experiment but replace the Silly Putty with a soft, non-elastic putty. You will have to pull the battering ram much farther back in order to knock over the block when the battering ram hits the non-elastic putty.
Explanation: When an object slows to a stop during a collision, it transfers all of its forward momentum to the surface it hits. If that object rebounds, it will then transfer additional forward momentum to the surface so that the object leaves with backward momentum.
Demonstration 3.2.7: Sending a Croquet Ball
Description: Two croquet balls are touching one another when one of the balls is hit sharply with a mallet. The struck ball immediately hits the second ball head on and comes to a stop. The second ball continues on with the momentum and energy of the first ball.
Purpose: To illustrate the transfers of energy and momentum that occur during a collision.
2 croquet balls
1 croquet mallet
Procedure: Place the two croquet balls side by side so that they almost touch. Now strike the outside surface of one ball firmly and briefly so that the ball travels directly toward the second ball. When the first ball hits the second ball, the first ball will come to a stop and the second ball will take over its motion.
Explanation: Croquet balls are highly elastic, so that when they collide, they exchange both momentum and energy. The first ball pushes on the second ball both as they approach one another and as they rebound. This relatively elastic collision allows the first ball to transfer virtually all of its momentum and most of its energy to the second ball and the second ball takes over the first ball's motion.
Follow-up: Try a similar experiment with pool or billiard balls and a cue stick. Also, experiment with an "executive toy," a toy (discussed below) with several steel balls that are suspended from a wooden frame so that they can swing into one another. If you pull one of the balls back and let it swing into the others, only the last ball in the chain will swing out. You can do this same experiment with a row of identical coins on a tabletop.
Demonstration 3.2.8: The Executive Toy
Description: A set of metal balls suspended from a frame exchange energy and momentum with one another.
Purpose: To illustrate the transfers of energy and momentum that occur during collisions.
1 executive toy
Procedure: Pull one ball out and let go of it. It will swing back toward its equilibrium position and collide with the other balls when it arrives there. Its momentum and energy will be conveyed from ball to ball until the far ball pops out of the line and continues the motion of the original ball. That last ball will swing up and out until gravity and its support strings reverse its motion and the process repeats in reverse.
Explanation: The metal balls are highly elastic and have equal masses. Like billiard balls, they exchange energy and momentum beautifully and almost completely. In this case, the first ball transfers essentially all of its forward momentum and all of its kinetic energy to the second ball during the impact, coming to a stop. The second ball does the same to the third ball, and so on until the last ball continues the first ball's motion.
Demonstration 3.2.9: Hardball and Less-Hardball Hammers
Description: Two identical looking hammers are used to pound a nail into a board. The hardball hammer works fine, but the less-hardball hammer merely bounces off the nail.
Purpose: To illustrate the enormous peak impact force that can arise when two hard objects collide.
1 hardball on with a mallet handle (you can buy a mallet handle and install it in a hardball with a hole drilled in it. Glue and friction will hold it in place, although you should always be careful not to let the ball fling off its handle).
1 less-hardball on with a mallet handle. These balls look and feel almost like hardballs, but they are slightly softer.
1 large-head nail.
Procedure: Have a student pound the nail in with the hardball hammer. It should be relatively easy to make progress. Now have the student try the less-hardball hammer. The hammer will just bounce off the nailhead and the nail won't make any progress into the board.
Explanation: Although the two ball-mallets look and feel nearly identical, the true hardball is much harder than the other ball. The true hardball therefore conveys all of its downward momentum to the nail in a much shorter period of time and with a much larger force--an impact force. Since the nail is being held in place by static friction, it won't make any progress into the board until the force exerted on it exceeds some large peak value. The hardball's impact force easily exceeds that threshold, but the other ball can't exert enough impact force to start the nail moving. Instead, the less-hard ball transfers its downward momentum too slow to the nail and subsequently bounces back up from the nail without driving the nail into the board.
Demonstration 3.2.10: A Baseball Bat's Center of Percussion
Description: A baseball bat, hanging by its handle from a support, is struck at various places with a rubber mallet. Only when the bat is struck at its center of percussion does the handle remain in place.
Purpose: To show that there is a special point on the bat, its center of percussion, at which you can hit the ball without causing the bat's handle to accelerate.
1 baseball bat
1 rubber mallet
Procedure: Attach the string to the bat's handle and hang the bat from the support. With the bat hanging motionless below the support, strike the bat firmly at various points on its business end. Only when you strike the bat on its center of percussion will the handle remain in place (although the bat's body will accelerate away from the impact and the bat will begin to rotate). If you hit the bat almost at its end, the handle will jerk toward the mallet. If you hit the bat near its middle, the handle will jerk away from the mallet. You can show this jerking motion by sticking the putty to the bat's handle. The bat will fling the putty in the direction of its jerk. When you hit the bat exactly at its center of percussion, the putty may still come off the bat because of vibrations, but it will drop more or less straight down.
Explanation: When you hit the bat, the bat's center of mass will accelerate away from the mallet but the bat will also begin to rotate about that center of mass. If you hit the bat at its center of percussion, these two motions will cancel at the handle and the handle itself won't accelerate.
Demonstration 3.2.11: A Baseball Bat's Vibrational Node
Description: A wooden baseball bat, hanging by a string from a support, is struck at several places with a rubber mallet. Only when it's struck at its vibrational node does the bat emit a clear "crack" sound. When struck at other places, the bat emits a buzzing sound.
Purpose: To show that a bat can vibrate and that you can avoid making it vibrate only by hitting it at its vibrational node.
1 wooden baseball bat
1 rubber mallet
Procedure: Attach the string to the handle of the bat and hang it from the support. Strike the bat a sharp blow with the mallet and listen to the buzzing sound it emits. When you hit the bat's vibrational node, there should be a significant change in the sound, with it emitting the sharp "crack" sound we associate with a solid impact. The bat's vibrational node should roughly coincide with its center of percussion.
Explanation: The bat vibrates in much the same way that a xylophone plate vibrates—the middle of the bat moves in the opposite direction from its two ends. That motion is its fundamental vibrational mode. This mode of vibration leaves two points on the bat motionless and these two vibrational nodes are located along its handle and part way along the business end of the bat. When you strike the bat at one of these nodes, you don't excite its fundamental vibrational mode and it thus emits very little sound. Any sound that the bat emits is at much higher frequencies because it involves higher order vibrational modes.
Follow-up: Why is a xylophone plate supported at two points that are each about half way between the middle and end of the plate?
Another Follow-up: Hold an 18" C-Thru plastic ruler horizontally by its middle and flap it up and down rapidly. You'll see that the middle and ends are anti-nodes and that it has a node part way toward each end.
Demonstration 3.2.12: Rotation and Translation During a Bounce
Description: A spinning basketball that's dropped on the floor leaps forward or backward after it hits.
Purpose: To show that friction between a ball and the surface it hits can cause the ball's rotational and translational motions to interact with one another.
1 basketball (or another large ball)
Procedure: Spin the basketball as you drop it and watch what happens when it hits the floor. It will leap forward or backward, depending on its direction of spin. Point out that the support force from the floor is directly upward, so that this effect must be due to friction between the ball's surface and that of the floor.
Explanation: The frictional force on the ball causes it to accelerate, increasing its translational motion. This same frictional force also produces a torque that slows the ball's rotational motion.
Demonstration 3.2.13: Balls Rolling Down a Ramp or the Importance of Properly Inflated Tires
Description: Two identical-looking balls roll down a ramp and the one that bounces poorly takes longer.
Purpose: To show that balls that bounce poorly also tend to waste energy as they roll.
1 happy ball
1 unhappy ball
1 hard-surfaced ramp
Procedure: Show the students that the two ball bounce differently by dropping them onto a hard surface. The unhappy ball will barely bounce at all while the happy ball will bounce nicely. Then ask the students to predict which of the two balls, if any, will reach the bottom of the ramp first. In all likelihood, they won’t have any firm answer. Simultaneously roll the two balls down the ramp from rest. The happy ball should reach the bottom well ahead of the unhappy ball.
Explanation: As the balls roll, their surface dent and undent continuously. The happy ball wastes little energy in this process while the unhappy ball wastes a considerable amount. This demonstration explains why poorly inflated tires lower a car’s gas mileage: they waste energy while denting and undenting, becoming hot and squandering gasoline.
Section 3.3 Carousels and Roller Coasters
Demonstration 3.3.1: The Experience of Weight
Description: You sit in a chair and describe how you experience your weight.
Purpose: To show that we experience weight in terms of the internal stresses involved in supporting the parts of our bodies.
Procedure: Sit in the chair and describe what you feel. You feel your neck supporting your head to keep your head from falling. You feel your shoulders supporting your neck. And all the way down to your behind being supported by the chair.
Explanation: We don't feel weight directly; we feel the forces that develop inside us when we try not to accelerate in response to our weight.
Demonstration 3.3.2: The Experience of Acceleration
Description: You sit in a chair on a wheeled cart and describe how you experience acceleration.
Purpose: To show that we experience acceleration in terms of the internal stresses involved in making the parts of our bodies accelerate together.
1 wheeled cart on which the chair will fit (or simply use an office chair that has its own wheel).
Procedure: Sit in the chair and have a student make you accelerate forward (briefly). Describe what you feel while you are accelerating. You feel your neck pushing your head forward to keep it accelerating along with the rest of you. You feel your shoulders pushing your neck forward. And all the way to your back, which is being pushed forward by the chair.
Explanation: We don't feel acceleration directly; we feel the forces that develop inside us when we try not to come apart as we accelerate.
Demonstration 3.3.3: Sweeping a Bowling Ball in a Circle
Description: A student tries to keep a bowling ball moving in a circle, using only a broom to guide it. She quickly discovers that she has to push it always toward the center of the circle.
Purpose: To show that uniform circular motion requires a centripetal acceleration caused by a centripetal force.
1 large ball (a bowling ball is ideal)
1 marker for the center of the circle
Procedure: Mark the center of your circle on the floor. Have a student use the broom to sweep the ball in a circular path around the marker at a steady pace. After getting the ball moving, she'll find that she has to keep pushing the ball toward the center of the circle. That requirement is somewhat unexpected and counter-intuitive, so the student will have to find it by trial and error.
Explanation: To keep moving steadily in a circle, an object needs a central force. The broom makes this need for a central force obvious because it doesn't exert much friction and can't mask the direction of the force it's exerting on the ball.
Demonstration 3.3.4: Swinging a Ball on a String
Description: A rubber ball attached to a string circles your head. The only force on the ball (ignoring gravity) is the inward pull of the string.
Purpose: To show that a centripetal force can cause uniform circular motion.
1 rubber ball attached to a string
Procedure: Swing the ball around your head on the string. Point out that the only horizontal force on the ball is the inward pull of the string. Point out that the ball is always accelerating toward your hand (the center of the circle) because of the inward pull of the string (a centripetal force). Ask the students what will happen if you let go of the string. They should recognize that it will immediately begin to travel in a straight line, continuing forward in the direction it was traveling at the moment you let go of the string. Show them that this is the case.
Explanation: Uniform circular motion involves a centripetal acceleration. For an object to travel in a circle at a uniform speed, it must be experiencing a centripetal force.
Demonstration 3.3.5: A Book-in-Hand Loop-the-Loop
Description: A book held in your open palm remains in your palm as you move it in a vertical circle, even though the book is beneath your palm as you pass through the top of that circle.
Purpose: To show that an object traveling in a circle is experiencing a centripetal acceleration and that that acceleration can exceed the acceleration due to gravity.
1 book (a paperback novel works just fine)
Procedure: Place the book on top of your open palm. Now move your palm quickly in a large vertical circle so that your palm is always facing the center of that circle. When you finish, your arm will have become twisted one full turn. If you do this motion quickly enough, the book will follow your palm and will remain pressed against it even as your hand travels over the top of the circle and the book is below your open palm. You can then circle backward to untwist your arm.
Explanation: As long as you make the book accelerate toward the center of the circle faster than the acceleration due to gravity, your palm will have to provide at least part of the centripetal force and the book will remain pressed against your palm.
Demonstration 3.3.6: Swinging a Wine Glass on a Pizza Pan
Description: A full wineglass remains in place on a pizza pan as you swing that pizza pan in a vertical circle at the end of a rope.
Purpose: To show that when an object on a platter is made to travel rapidly in a circle, the object experiences a large centripetal acceleration and needs a large centripetal force from the platter. If that centripetal acceleration exceeds the acceleration due to gravity, then the platter will have to push inward on the object and the object will push back on the platter. Even a liquid (wine) in the object will push against the platter and remain in the object.
1 wineglass (or a brandy snifter because a shorter stem makes the starting and stopping easier).
1 pizza platter
red wine (or red disappearing ink: about 1/4 tsp. of phenolphthalein in 1 liter water, with just enough sodium hydroxide—about 1/16 tsp.—to turn it pink. When exposed to air, carbon dioxide gradually deactivates the sodium hydroxide and renders the mixture colorless.)
Procedure: Attach three pieces of rope to the edge of the pizza platter at three evenly spaced locations and join those ropes together about 0.5 m above the platter. Attach a single rope about 1 m long to the three joined ropes. You should be able to hold that single rope and swing the platter in a vertical circle, and the platter's surface should always face the center of the circle. After some practice with non-fragile objects in the platter, particular with a cup of water, try the wineglass. Starting and stopping are much harder than keeping the wineglass going. You must always let the platter swing freely during the starting and stopping—it will lag behind your hand briefly as you start and it will swing past your hand briefly as you stop. If you let it swing properly, the wineglass will remain in place on the platter and everything will go well. Make sure that you start aggressively enough that you go over the top of the circle the first time at full speed. If you go slowly over the top of the circle, you'll have a disaster.
Explanation: Traveling in a circle requires a centripetal force. The platter exerts that centripetal force on the wineglass and the wineglass exerts that centripetal force on the wine. Since the wineglass pushes inward on the wine, the wine pushes outward on the wineglass and the two remain pressed against one another, even as they pass upside-down over the top of the circle.
Demonstration 3.3.7: Ball on Loop-the-Loop Track
Description: A car or ball rolls down the hill of a track and then around a circular loop-the-loop. It remains pressed against the track, even at the top of the loop-the-loop.
Purpose: To show that an object traveling in a circle is undergoing centripetal acceleration and requires a centripetal force.
1 car or ball
1 toy track with a hill and a loop-the-loop
Procedure: Assemble the track so that you have a hill and a loop-the-loop. Make sure that the hill is high enough (at least 5/2 as tall as the loop-the-loop) that the car or ball will move fast enough to remain on the loop-the-loop. Now roll the car or ball down the hill and let it go around the loop-the-loop. If it's traveling fast enough, it will remain pressed against the track, even at the top of the loop-the-loop. Now repeat this experiment from lower points on the hill and show that without sufficient speed, the centripetal acceleration will be less than the acceleration due to gravity and the car or ball will begin to fall rather than follow the track.
Explanation: As long as the centripetal acceleration of the car or ball exceeds the acceleration due to gravity, the track will have to provide at least part of the centripetal force on the car or ball and the two will push against one another. Even at the top of the track, the car or ball will remain pressed against the track.
Demonstration 3.3.8: Spin Drying
Description: A wet towel is swung rapidly in a circle, causing the water to leave it and travel in a straight line.
Purpose: To show how a spin dryer works.
1 wet towel
Procedure: Hold one end of the towel in your hand and swing it rapidly around in a circle. Water will spray off the other end of the towel and travel in a straight line (though it will also fall). Swing it both in a horizontal plane and a vertical plane to show that this effect is essentially independent of gravity.
Explanation: For the far end of the towel to travel in a circle, it must experience a centripetal force. This force is provided by your hand and by the tension in the towel. The water, which is not very well attached to the towel, can break free of the towel and travel in a straight line.
Demonstration 3.3.9: Break a String with Forces Due to Acceleration
Description: A small weigh hangs easily from a piece of thin string until you try to accelerate the weight too quickly. The string breaks.
Purpose: To demonstrate that a force is needed to cause acceleration.
1 piece of thin string.
1 weight that can be held relatively easily by the string.
Procedure: Hang the weight from the string to show that the string is strong enough to support it. Now show that if you try to accelerate the weight rapidly in any direction, the force required may be more than the string can tolerate. You should be able to break the string by accelerating the weight in any direction, even downward. You can also drop the weight and let it pull taut and break the string to show that an object moving downward can also be accelerating upward.
Explanation: The force an object exerts on a string is not limited to its weight. If you are causing that object to accelerate, it will pull back on you with a force equal to its mass times its acceleration (in addition to any forces needed to support its weight). If you can’t tolerate that much force, you’re in trouble.