. How can you measure weight and/or mass through distance?
With a spring scale, the distortion of the spring is proportional to how much force it is exerting. If you measure that distortion, you can determine how hard it is pulling or pushing on whatever is attached to it. If it's supporting the weight of an object, you can determine that object's weight by measuring how far the spring distorts while supporting it.
. If a spring scale measures weight, what does a mass scale use to figure out mass? Are weight and mass measured the same way?
A spring scale measures weight. It does this by reporting how much upward force it needs to exert on an object to keep that object from accelerating. Since this upward force exactly balances the object's weight (assuming the object isn't accelerating), the upward force reported by the scale is exactly equal to the object's weight. If the scale reports that the object has a certain mass (in kilograms), then it is taking advantage of the fact that, near the earth's surface, each kilogram of mass weighs 9.8 newtons. But it is still measuring weight and using the relationship between mass and weight to determine the object's mass. If you were to move the "mass" scale to a new location, such as the moon's surface, the scale would read incorrectly because the relationship between mass and weight would have changed.
. If you hang a weight from a scale ten feet up and the weight descends 2 feet, is the loss in gravitational potential energy equal to the elastic potential energy gained?
Not quite. When you first let go of the weight, it falls freely because the spring isn't stretched and doesn't exert any upward force on the weight. The spring won't support the weight fully until the weight has fallen 2 feet. By then, the weight has acquired a lot of kinetic energy and it overshoots the 2-foot level. The weight begins to bounce up and down around that 2 foot point and takes a while to settle down. The weight is vibrating up and down because it has too much energy at the 2-foot point. Eventually, it converts its extra energy into thermal energy and becomes motionless at the 2-foot point. At that point, it has turned exactly 1/2 of the missing gravitational potential energy into elastic potential energy and the other 1/2 into thermal energy. This 50/50 conversion is a remarkable result related to the exact proportionality between the spring's distortion and the force it exerts.
. If you lifted an object with a hanging scale on earth and it read 15 N, would it read the same on Jupiter? What about the gravitational force pulling the object down? Wouldn't that alter the reading on the scale? Would you have to calibrate another scale to measure mass on Jupiter?
No, the scale would not read the same on Jupiter, and there would be nothing wrong with the scale! On Jupiter, the object would simply weigh more than on earth. Its mass wouldn't have changed and it would still contain the same number of atoms, but Jupiter would pull on it harder. As a result, the scale would have to pull upward on it harder and the scale would read a larger number of newtons. You wouldn't want to recalibrate the scale because it would be doing its job: it would correctly report that the object weighed about 40 N.
. Is it true that gravity is stronger at the north pole than at the equator. Does that mean that a person would be able to jump higher at the equator?
Yes. Because of its rotation, the earth isn't quite spherical and people near the poles of the earth experience stronger gravity than at the equator. At the equator, they would experience an apparent weight that was 1% less than at the poles and would be able to jump higher as a result. The Olympic committee should take note.
. When you transfer momentum between two objects, why is it that the change in total momentum is 0?
Suppose you are standing motionless on extremely slippery ice. If you now take off your shoe and throw it northward as hard as you can, you will transfer momentum to it. Since you and your shoe were initially motionless, your combined momentum was 0. Neither of you nor the shoe was moving, so the product of mass times velocity was 0. But after you throw the shoe, both you and the shoe have momentum. Your momentum is equal to your mass times your velocity, so your momentum points in the direction you are going. The shoe also has momentum, equal to its mass times its velocity. But since it is heading in the opposite direction from you, it has the opposite momentum from you. Together, your combined momentum remains exactly 0—it didn't change. In general, momentum is transferred from one object to another so that any change in momentum in one object is always compensated for by an opposite change in momentum in the other object.
. How do rubber bouncing balls work? Does the table exert more force than is applied, causing an upward acceleration?
The table never pushes up on the ball harder than the ball pushes down on the table. That would violate Newton's third law and is just not the way our universe works. As the ball strikes the table, the two objects dent. The ball dents most and has work done on its surface—the table pushes the surface inward and work is force times distance in the direction of that force. The ball stores this work/energy as a deformation of its elastic surface and a compression of the air inside the ball. The ball then rebounds from the table as this stored energy reemerges as kinetic energy in the ball. Throughout the bounce, the upward force that the table exerts on the ball is much larger than the ball's downward weight. As a result, the ball accelerates upward the whole time. It starts the bounce heading downward and finishes the bounce heading upward.
. If all the laws of physics always happen the same, then what relevance does the frame of reference have?
If you observe the world from an inertia frame of reference—meaning that you aren't accelerating—then all of the laws of physics will apply properly to the objects you see. Energy will be conserved during activities, momentum will be transferred between objects without being created or destroyed, and so on. So it's true that any inertial frame of reference will do. However, there is often a "best" reference frame from which to observe a situation. A good example of this is the situation in which a ball bounces from a bat. The best inertial reference frame from which to watch that bounce is the frame of the moving bat. In that special inertial reference frame, the bat doesn't move and the ball bounces off the stationary bat.
. If I'm a WWF Wrestler, and I sling-shot myself off the ropes, and my momentum carries me as I put a flying shoulder block on my opponent, is my momentum conserved and do I feel any momentum against me?
As you bounce off the ropes, you exchange momentum with the ropes (and the earth). As a result, you normally reverse your momentum and head back into the ring. When you hit your opponent, you begin to exchange momentum with him/her. If you hit your opponent feet first and jump backward, you will reverse your direction of travel again and your opponent will receive an enormous amount of forward momentum. All of this transfer of momentum means that your personal momentum will change often but the total momentum of the earth and its population won't change. That momentum will just be rearranged amount the various objects.
. If you throw a dead ball at a baseball, would the baseball not roll as far as if you throw a super ball at it?
Your right. The dead ball transfers less momentum to the baseball than the lively super ball does. That's because the dead ball transfers momentum only one, essentially coming to a stop on the baseball's surface. The bouncy ball transfers momentum twice because it also pushes on the baseball as it rebounds. Overall the baseball receives more momentum (and also more energy) from the super ball than from the dead ball. The dead ball turns much of the collision energy into thermal energy.