. Why do you feel no acceleration in free fall, even though you are accelerating?
This wonderful question has many answers. The first, and most direct, is that you do feel the acceleration. You feel an upward fictitious force (not a real force at all, but an effect of inertia) that exactly balances your downward weight. The feeling you experiences is "weightlessness." That's why your stomach feels so funny. You're used to having it pulled downward by gravity but the effect of your fall is to make it feel weightless.
. Why does a ball fall 4.9 meters during its first second of falling?
As a simple argument for that result, think about the ball's speed as it falls: it starts from rest and, over the course of 1 second, it acquires a downward speed of 9.8 m/s. Its average speed during that first second is half of 9.8 m/s or 4.9 m/s. And that is just how far the ball falls in that first second: 4.9 m. By holding the ball 4.9 m above the floor, you can arranged for it to hit one second after you drop it.
. Why does an object accelerate when it changes direction?
What you mean by "changes direction" is that the direction part of its velocity changes. For example, instead of heading east at 10 m/s (or 10 miles-per-hour, if that feels more comfortable), it heads north at 10 m/s (or 10 miles-per-hour). This change in direction involves acceleration. The car must accelerate toward the west in order to stop heading east, and it must accelerate toward the north in order to begin moving north. Actually, it probably does both at once, accelerating toward the northwest and shifting its direction of motion from eastward to northward.
. Why is 45° above horizontal the ideal angle to throw something the greatest distance if gravity is acting on the vertical direction but not the horizontal?
The 45° angle is ideal because it gives the ball a reasonable upward component of velocity and also a reasonable downfield component of velocity. The upward component is important because it determines how long the ball will stay off the ground. The downfield component is important because it determines how quickly the ball will travel downfield. If you use too much of the ball's velocity to send it upward, it will stay off the ground a long time but will travel downfield too slowly to take advantage of that time. If you use too much of the ball's velocity to send it downfield, it will cover the horizontal distances quickly but will stay of the ground for too short a time to travel very far. Thus an equal balance between the two (achieved at 45°) leads to the best distance. Note that this discussion is only true in the absence of air resistance.
. Why is force = mass * acceleration an exact relationship (i.e. why not force = 2 * mass * acceleration)?
The answer to this puzzle lies in the definition of force. How would you measure the amount of a force? Well, you would push on something with a known mass and see how much it accelerates! Thus this relationship (Newton's second law) actually establishes the scale for measuring forces. If your second relationship were chosen as the standard, then all the forces in the universe would simply be redefined up by a factor of two! This redefinition wouldn't harm anything but then Newton's second law would have a clunky numerical constant in it. Naturally, the 2 is omitted in the official law.
. Why on Pg. 6, 2nd full paragraph, it says the car is accelerating if the slope of the road changes but in the "not accelerating" list it says a bicycle going up a hill is not accelerating. Aren't those the same situation?
Here is why the two situations are different:
In the first case, the car is traveling on a road with a changing slope. Because the road's slope changes, the car's direction of travel must change. Since velocity includes direction of travel, the car's velocity must change. In short, the car must accelerate. Picture a hill that gradually becomes steeper and steeper—the car's velocity changes from almost horizontal to almost vertical as the slope changes.
In the second case, the bicycle is climbing a smooth, straight hill at a steady speed. Since the hill is smooth and straight, its slope is not changing. Since the bicycle experiences no change in its direction of travel or its speed, it is traveling at a constant velocity and is not accelerating.
. How do you push a shopping cart and have the cart exert the same force on you, if you are still traveling forward? Friction? Air Resistance?
When you push a shopping cart straight forward down an aisle, you are pushing it forward and it is pushing you backward. If nothing else were pushing on the two of you, the cart would accelerate forward and you would accelerate backward. But the cart is experiencing friction and air resistance, both of which tend to slow it down. They are pushing the cart backward (in the direction opposite its motion). So you must keep pushing it forward to ensure that it experiences zero net force and continues at constant forward velocity. As for you, you need a force to keep yourself heading forward; otherwise the cart's backward force on you would slow you down. So you push backward on the ground with the soles of your shoes. In return, the ground pushes on you (using friction) and propels you forward. As a result, you also experience zero net force and move forward at constant velocity.
. How does a surface know how hard it must push upward on an object to support that object?
If you put a piano on the sidewalk, the piano will settle into the sidewalk, squeezing the sidewalk's surface until the sidewalk stops it from descending. At that point, the sidewalk will be pushing upward on the piano with a force exactly equal in magnitude to the piano's downward weight. The piano will experience zero net force and will not accelerate. It's stationary and will remain that way.
But if the sidewalk were to exert a little more force on the piano, perhaps because an animal under the sidewalk was pushing the sidewalk upward, the piano would no longer be experiencing zero net force. It would now experience an upward net force and would accelerate upward. The piano would soon rise above the sidewalk. Of course, once it lost contact with the sidewalk, it would begin to fall and would quickly return to the sidewalk.
For an example of this whole effect, put a coin on a book. Hold the book in your hand. The book is now supporting the coin with an upward force exactly equal to the coin's weight. Now hit the book from beneath so that it pushes upward extra hard on the coin. The coin will accelerate upward and leap into the air. As soon as it loses contact with the book, it will begin to fall back down.
Thus, if the sidewalk pushed upward too hard, the piano would rise upward and leave the sidewalk's surface and if the sidewalk pushed upward too weakly, the piano would sink downward and enter the sidewalk's surface. A balance is quickly reached where the sidewalk pushes upward just enough to keep the piano from accelerate either up or down.
. If a falling egg weighs only 1 newton, how can it exert a force of 1000 newtons on a table when it hits?
As the egg falls, it is experiencing only one force: a downward weight of 1 N. But when it hits the table, it suddenly experiences a second force: an upward support force of perhaps 1000 N. The table is acting to prevent the egg from penetrating its surface. The net force on the egg is then 999 N, because the upward 1 N force partially cancels the downward 1000 N force. If the egg could tolerate such forces, it would accelerate upward rapidly and wouldn't enter the table's surface. Because the egg is fragile, it shatters. The force that the egg exerts on the table is also 1000 N, this time in the downward direction. The egg and table push on one another equally hard. The table doesn't move much in response to this large downward force because it's so massive and because it's resting on the floor. But if you were to put your hand under the falling egg, you would feel the egg push hard against your hand as it hit.
. If every force always has an equal and opposite force pushing against it (like the bowling ball and your arm in today's lecture), how can anything at all accelerate? Wouldn't forces always
cancel each other out?
The two equal but opposite forces are being exerted on different objects! In many cases, those two objects are free to accelerate independently and they will accelerate—in opposite directions! For example, when I push on a bowling ball, it pushes back on me with an equal but opposite force. If my force on the bowling ball is the only force it experiences, it will accelerate in the direction of my force on it. Since it exerts an opposite force on me, I will accelerate in the opposite direction—we will push apart!