1. The starting gun goes off and you step on the accelerator. Your car practically leaps forward in response. You find yourself pressed deeply into the well-upholstered seatback of the Chevy.

(A) What force, if any, is pushing backward on you so that you dent the seatback?
(B) What force, if any, is pushing forward on you so that you accelerate forward?

Answer: (A) There is no force pushing you backward. (B) The seatback is pushing you forward.

Why: The car is trying to make you accelerate forward with it. To cause that acceleration, it has to exert an unbalanced forward force on you, probably using its seatback for most of that force. While you feel as though you're pushed backward during this acceleration, there is no real force pushing you backward. It's merely you experiencing your inertia.

2. As you approach the first left turn, you begin steering hard to the left and your car swings smoothly around that corner. During the left turn,

(A) what force, if any, is pushing outward on your body (toward the right)?
(B) what force, if any, is pushing inward on your body (toward the left)?

Answer: (A) There is no force pushing you outward. (B) The car is pushing you inward.

Why: The car is trying to make you accelerate leftward with it. To cause that acceleration, it has to exert an unbalanced leftward force on you, probably using friction from the seat or support forces from other parts of the car's interior. While you feel as though you're pushed outward during this acceleration, there is no real force pushing you outward. It's merely you experiencing your inertia again.

3. As you drive straight forward at a steady speed, you pluck your lucky quarter from your pocket and toss it straight up into the air inside the car. It rises to a peak and drops neatly into your hand. Your close friend, sitting in the stands and cheering you on, watches you drive by toward the right at this very moment and sees the coin rise and fall. From your friend’s perspective or “frame of reference,” what does the coin’s motion look like while it is above your hand?

Answer: The coin travels in an arc (or a parabolic arc).

Why: From your friend's perspective, the coin left your hand traveling both upward and forward. It looks as though you threw it upward and forward. As a result, it travels in the parabolic arc of a thrown coin. It rises and falls because of gravity, but it coasts forward because of inertia alone.

4. You come to a moderate bump in the road and rise quickly up, over, and down the bump’s smoothly curving surface. The car’s tires never quite leave the road and you never quite leave your seat. Nonetheless, you feel a strange series of changes in what you perceive as your “weight.” When during the trip over this bump do you feel

(A) heaviest?
(B) lightest?
(C) your normal weight?

(Note: your answer doesn’t have to be something like “as you go up” or “as you go down.” It can be something like “at the moment your horizontal velocity reaches its maximum forward value.”)

Answer: (A) You feel heaviest when you are accelerating upward fastest. (B) You feel lightest when you are accelerating downward fastest. (C) You feel your normal weight whenever you are not accelerating.

Why: You feel fictitious "forces" whenever you accelerate and they seem to pull you opposite your acceleration. Thus when you accelerate upward fastest, you feel pulled downward hardest and seem the heaviest. And when you accelerate downward fastest, you feel pulled upward hardest and seem the lightest. Whenever you are not accelerating at all, you simple experience your normal weight.

5. You come to a sudden drop off in the road. Your car was heading forward horizontally when the road abruptly drops 3 feet before continuing on horizontally. Your Chevy is airborne before landing hard on the rigid asphalt surface. It actually bounces back into the air once! The Chevy’s tires and its spring suspension (huge coil springs between the wheels and the car body) have allowed the Chevy to act like a ball so that it bounces off the roadway! Fortunately, you only bounce once before settling back onto the road. (Imagine trying to steer if the car continued to bounce repeatedly.) You have been saved from an embarrassing and dangerous pogo-stick-like ride down the road by the Chevy’s shock-absorbers. These shock-absorbers damp out the bouncing by dealing successfully with

(A) which conserved quantity that is involved in a bounce?
(B) What did the shock absorbers do with that conserved quantity?
(C) Do the shock absorbers affect the car’s coefficient of restitution and, if so, do they increase it or decrease it?

Answer: (A) Energy. (B) They wasted it (probably as thermal energy). (C) Shock absorbers reduce the car's coefficient of restitution.

Why: During a bounce, the car has no difficulties exchanging momentum with the ground... all it takes is a force exerted on the ground for a time. But the car cannot transfer much energy to the ground because the ground won't move much and the car therefore cannot do much work on it. The car must therefore deal with its energy all by itself. The shock absorbers help damp out the bouncing by wasting the bouncing energy. Without the shock absorbers, the car will hop up and down for a long time, waiting for the energy to gradually transform into thermal energy via friction and air resistance. But the shock absorbers speed the conversion. In doing so, they make the car less lively and reduce its coefficient of restitution. The car goes from being a bouncy ball to a beanbag.

6. While racing is supposed to be a non-contact sport, a few minor collisions are typical in a race. Your arch-rival's car (there’s always an arch-rival, isn’t there?) bumps your car from behind. Your friend in the stands watches the bump occur. From your friend’s perspective, you are heading to the right at 100 mile-per-hour and your rival’s car is heading to the right at 110 mile-per-hour. Predicting the outcome of this collision would be difficult if it weren’t for an odd coincidence: your two cars have exactly equal masses and the bumpers have exactly zero coefficients of restitution. The cars coast into each other, bump, and then continue on with their bumpers touching! One conserved quantity of motion has been shared equally between the two cars. Another conserved quantity has been partially wasted and the remaining portion of that quantity distributed equally between the two cars.

(A) Which conserved quantity was shared equally?
(B) Which conserved quantity was partially wasted and then distributed equally?
(C) From your friend's perspective, how fast are the two cars traveling to the right just after they bump?

Answer: (A) Momentum was shared equally. (B) Energy was partially wasted and then distributed equally. (C) The two cars travel onward at 105 miles-per-hour.

Why: You can't hide momentum or waste it, so the two cars have to share what they have directly. Energy, however, can be hidden or wasted and these occur during the bounceless collision between the two cars. From your perspective, the rival's car approaches you at 10 miles-per-hour, hits, and doesn't bounce at all. Your car receives a forward impulse and picks up forward momentum, and therefore increases speed. The rival's car receives a backward impulse and picks up backward momentum, and therefore loses speed. Because you share the momentum equally in the end, each car ends up with the average initial momentum. And because you both have the same mass, each car ends up with the average initial initial velocity as well: 105 miles-per-hour.

7. Your rival never manages to pass you and you win the race! Your friend from the stands joins you in the Chevy's passenger seat as you drive fast in a tight circle around the dirt parking lot next to the track. You are steering steadily toward the left and have completed 3 full circles when your friend reaches into your pocket and takes out your lucky quarter. Your friend tosses that coin straight up (from your friend’s perspective) just as the car passes through the northernmost point on its circular path. The coin appears to shift rapidly in a strange direction and does not return to your friend’s hand.

(A) From your friend’s perspective, in which horizontal direction did the coin begin traveling after it left your friend’s hand? (ignoring its rise and fall)
(B) From the perspective of an observer standing in the parking lot, in which horizontal compass direction did the coin begin traveling after it left your friend’s hand?
(C) Describe in a few words why the coin didn’t return to your friend’s hand.

Answer: (A) Your friend sees the coin drift toward the right. (B) The observer sees the coin begin traveling west. (C) The coin fails to return to your friend's hand because the car and your friend's hand drive out from under the coin.

Why: Your friend is accelerating toward the left, so the coin (which is following its inertia path) appears to drift toward the right. The observer in the parking lot see your car heading westward at the moment it passes through its northern-most position. The coin therefore leaves your friend's hand with a westward horizontal component of velocity. This coin coasts westward as it rises and falls, but it misses your friend's hand on the way down. That's because your friend's hand accelerated out from under the coin. The coin did what comes naturally to it, at least horizontally: it coasted. Your friend's hand didn't coast... instead, it was yanked leftward by the car as the car accelerated and it moved out from under the coin.

8. The quarter didn’t bounce at all when it hit the surface of the dirt parking lot. Metal is normally pretty elastic, so why didn’t the coin bounce?

Answer: The soft dust did most of the denting during the bounce and it wasted its share of the collision energy.

Why: The coin might bounce nicely when dropped on a hard surface, but it has no opportunity to show its stuff when dropped on a soft surface like dust. Instead, the dust is responsible for the bouncing and the dust does a lousy job. During the collision between the coin and the dust, the dust does virtually all of the denting and receives almost all the collision energy. The dust wastes this energy immediately as thermal energy, via internal friction between the dust particles, and the coin barely rebounds at all.