Problem Set #3
Goal of Problem Set #3: This assignment is meant to help you understand:
  1. bouncing behavior in springs, balls, and other elastic objects,
  2. relative motion and the interactions between objects in relative motion,
  3. connections between translational and rotational motions,
  4. connections between acceleration and force,
  5. the way we perceive acceleration.
Your love of speed simply will not be denied and you have joined the racing circuit. But with limited sponsorship, namely your job reshelving books in the library, you can't afford to join NASCAR or Formula 1 Racing. Instead, you put new tires and paint on your great-aunt’s old Chevy and head off to the local car track. The track has turns and bumps and everything anyone could want in the way of speed and competition. You’re wearing just the right clothes and you look so unbelievably cool that I almost can’t finish this problem set… well, I did say “almost.”
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?
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)?
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?
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.”)
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?
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?
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.
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?
Though you're not superstitious at all, you stop the car to retrieve the mystical coin and then drive off into the sunset. Even if you can't get an internship this summer or an academic-related job when you graduate, you can always turn to racing as a career.