Due Monday, February 6, 1995, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1:
Two cars are driving at 88 km/h (55 miles-per-hour) toward an intersection. A 1500 kg touring sedan is heading east and a 700 kg subcompact is heading north. The subcompact has a green light and drives into the intersection. The tired driver of the touring sedan runs the red light and crashes directly into the driver's side of the subcompact. The subcompact experiences a sudden, strong force to its right (toward the east).
(A) Which car experiences the largest force due to the collision?
(B) Which car experiences the largest acceleration due to the collision?
(C) Which car is most likely to be thrown off the roadway because of the collision?
(D) If the force on the subcompact is directly toward that car's right (directly toward the east), what happens to the north/south component of the subcompact's velocity?
(E) If the sedan loses 10,000 kg-m/s of momentum to the east due to the collision, what is the subcompact's change in momentum due to the collision? (Note: the kg-m/s is the SI unit of momentum)
Question 2:
Cable cars have ridden the hills of San Francisco for generations. As they ascend the hills, the cable cars are pulled up by moving, underground cables. As they descend those hills, the cable cars are held back by those same cables.
(A) As the cable pulls the car uphill, which does work on which? As the cable lowers the car downhill, which does work on which?
(B) On a gentle hill, the car rises 1 m in height as it travels 10 m along the road. On a second, steeper hill, the car rises 1 m in height as it travels 5 m along the road. If the cable must exert 3,000 N of force on the car to pull it up the gentle hill at constant velocity, how much force will be needed to pull the car up the steeper hill at constant velocity?
(C) The car now begins to descend the gentle hill. How much force is needed to keep the car from accelerating downhill and in which direction does the cable exert its force on the car?
(D) What is the weight of the cable car in newtons? (Hint: how hard would the cable have to pull if the hill were straight up?)
(E) What is the mass of the cable car in kilograms?
Question 3:
Three children are at a playground, playing with a seesaw. Two of the children are 3 years old and each has a mass of 15 kg; the third child is 7 years old and has a mass of 30 kg. The seesaw is made of a high-tech low-mass plastic, so that its mass can be ignored throughout this problem. The seesaw's pivot is in the middle of the board. The two 15 kg children sit together at the east end of the seesaw and the 30 kg child sits at the west end.
(A) The seesaw balances, meaning that it experiences no net torques when the children and the seesaw are not touching the ground. Describe the nature of any possible motion of the seesaw during the periods when the children and the seesaw are not touching the ground.
(B) What happens to the seesaw if the 30 kg child at the west end pushes downward on the ground?
(C) One of the 15 kg children loses interest (as 3 year olds are wont to do) and jumps off the board while the seesaw is exactly horizontal. What happens to the seesaw and the other 2 children?
(D) The two remaining children decide to continue playing on the seesaw. If the 15 kg child stays at the east end of the seesaw, exactly where should the 30 kg child sit in order for the seesaw to balance?
(E) The other 15 kilogram child returns and sits on the middle of the board, right above the pivot. The child has essentially no effect on the seesaw. Why not?
Question 4:
An escalator is essentially a moving staircase. The individual steps are supported by metal tracks that run on either side of the escalator. These steps follow one another in a complete loop, driven by an electric motor. When you step onto an escalator at the ground floor, it soon begins to carry you upward and forward at a constant velocity toward the second floor.
(A) While you are moving toward the second floor at a constant velocity, what is the net force exerted on you by all outside forces (specify the amount and the direction of the net force)?
(B) You know that gravity gives you a weight in the downward direction. What force does the escalator exert on you as you move toward the second floor at a constant velocity (specify the amount and the direction of force)?
(C) Is the escalator doing work on you as you move toward the second floor?
(D) As you first step onto the escalator, you begin to accelerate toward the second floor. Is the net force exerted on you by all outside forces the same as in part (A)?
(E) If the rapidly-moving escalator suddenly stopped moving, you would be thrown forward and might even fall over. What causes you to be thrown forward?
Question 5:
You are seated in a crowded bus that has stopped at a bus stop. Two people board the bus, one wearing rubber-soled shoes and one wearing inline skates (roller skates - i.e. no friction). They both have to stand in the middle of the aisle and neither one holds onto anything.
(A) The bus driver is new and the bus leaps forward from the bus stop. Which way does person wearing inline skates move in relationship to the bus?
(B) The bus is accelerating forward as it pulls away from the bus stop. Why doesn't the person wearing inline skates accelerate with the bus?
(C) The person wearing rubber soled shoes remains in place as the bus starts moving. What provides the force that caused that person to accelerate with the bus?
(D) Once the bus has reached a constant velocity (it is traveling along a straight road at a steady pace), the person wearing inline skates is able to stand comfortably in the aisle without rolling anywhere. What is the net force on the person wearing skates?
(E) The driver accidentally runs into a curb and the bus stops so abruptly that everything slides forward, including the person wearing rubber soles shoes. In stopping quickly, the bus experiences an enormous backward acceleration. Why doesn't the person wearing rubber-soled shoes accelerate backward with the bus?