b.) Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are
constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward
slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck
safely to a halt. Suppose a gravel ramp slopes upward at 6.0° and the coefficient of friction is 0.40.
Find the length of a ramp that will stop a 15,000 kg truck that enters the ramp at 35 m/s (about 75
mph). (10 pts)
Problem 1
a.) A 1000 kg car climbs a 5.0° slope at a constant velocity of 80.0 km/h. Assuming that air resistance
may be neglected, at what rate must the engine deliver energy to the drive wheels of the car? Express
your answer in kW. (10 pts)
Problem 2
This problem is related to the Air Track Collisions lab. Suppose two gliders of equal masses, m, move
toward each other at equal velocities, v, as shown. One of the gliders has a massless spring attached to
it with spring constant k so that the gliders bounce off each other. Assume there is no friction.
a.) In terms of m, v and k, compute Δx, the maximum amount of compression that occurs in the
spring. (4 pts)
b.) In terms of m, v, and k, what is the maximum force experienced by glider 1 (magnitude and
direction)? (4 pts)
c.) What is the magnitude and direction of the impulse felt by glider 1? (4 pts)
d.) Make an approximate plot of the force felt by glider 1 as a function of time. (Don’t try to come
up with an equation for F(t) . There’s no need to put units on the time axis.) (4 pts)
e.) Estimate the duration, Δt, of the impact. State any assumptions that you make. (4 pts)
Problem 3
A flywheel of mass M = 150 kg and radius R
=2.0 m rotates about a vertical axis through its
center of mass. The flywheel is in the shape of
a hollow disk so its moment of inertia is I =
MR2
.
a) The flywheel is initially rotating with an angular speed of 100 revolutions per minute (rpm). Find
the initial kinetic energy of the flywheel. (4 pts.)
b.) Find the angular momentum of the flywheel (magnitude and direction). (4 pts)
c) The flywheel is stopped by applying a brake pad to the rim with force F. The coefficient of kinetic
friction between the brake pad and the flywheel is µk = 0.25 and the wheel stops rotating after 10 s.
Find the magnitude of the force F. (4 pts.)
d.) What is the torque (magnitude and direction) on the flywheel? (4 pts)
e.) Find the work done by the force on the flywheel (make sure to indicate whether the work is
positive or negative) (4 pts.)
Problem 4
Timbie and Chung want to determine whose car is more massive. They are advised by Physics 207
students to find out the answer by colliding the cars together.
In experiment 1, Timbie’s car, with mass mT, is at rest when Chung’s car, mC crashes into it with
initial velocity vi. After the impact the two cars remain locked together and move with velocity vf.
In experiment 2, the cars are pulled apart from each other and collided again, this time with Chung’s
car at rest and Timbie’s crashing into it with the same initial velocity, vi, as in experiment 1. The cars
remain locked together after the impact and this time move with velocity vf′.
a.) In experiment 1, what is the ratio of the final kinetic energy to the initial kinetic energy? Express
your answer in terms of mT and mC. (7 pts)
b.) Using the results of both experiments, what is the mass of mT in terms of mC, vf, and vf′? (7pts)
Now for a different problem:
c.) A 1.6 kg particle moving along the x-axis experiences the net force shown in the figure. The
particle’s velocity is 4.0 m/s in the positive x direction at x = 0 m. What is its velocity at x = 2 m? (6
pts)
Measurement # Speed (m/s)
1 36
2 36
3 35
4 37
5 35
6 37
7 34
8 38
9 36
Assume that each measurement is independent and distributed according to a Gaussian distribution.
a.) What is your best estimate of the speed of the football and its standard deviation? (10 pts)
b.) Based on these measurements, what is your best estimate of the kinetic energy of the ball and its
standard deviation (i.e. the spread in the distribution of this derived quantity)? (10 pts)
Problem 5
Suppose you want to compute the kinetic energy of a football thrown by Bret Favre. You measure the
mass, m, of the football on a two-pan balance in the lab and determine that the mean mass is 0.40 kg
with a standard deviation of 0.02 kg. You measure the speed, s, of the football (measured off your TV
screen in instant replay mode) multiple times and record the values given in the table below
Sample Solution
