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Homework Problems
1. An object is observed to be moving at constant speed in a certain direc-
tion. Can you conclude that no forces are acting on it. Explain. [Based on a
problem by Serway and Faughn.]
2. A car is normally capable of an acceleration of 3 m/s
2
. If it is towing a
trailer with half as much mass as the car itself, what acceleration can it
achieve. [Based on a problem from PSSC Physics.]
3. (a) Let T be the maximum tension that the elevator's cable can with-
stand without breaking, i.e. the maximum force it can exert. If the motor is
programmed to give the car an acceleration a, what is the maximum mass
that the car can have, including passengers, if the cable is not to break. (b)
Interpret the equation you derived in the special cases of a=0 and of a
downward acceleration of magnitude g.
4 . A helicopter of mass m is taking off vertically. The only forces acting
on it are the earth's gravitational force and the force, F
air
, of the air pushing
up on the propeller blades. (a) If the helicopter lifts off at t=0, what is its
vertical speed at time t. (b) Plug numbers into your equation from part a,
using m=2300 kg, F
air
=27000 N, and t=4.0 s.
5. In the 1964 Olympics in Tokyo, the best men's high jump was 2.18
m. Four years later in Mexico City, the gold medal in the same event was
for a jump of 2.24 m. Because of Mexico City's altitude (2400 m), the
acceleration of gravity there is lower than that in Tokyo by about 0.01 m/s
2
.
Suppose a high-jumper has a mass of 72 kg.
(a) Compare his mass and weight in the two locations.
(b) Assume that he is able to jump with the same initial vertical velocity
in both locations, and that all other conditions are the same except for
gravity. How much higher should he be able to jump in Mexico City.
(Actually, the reason for the big change between '64 and '68 was the
introduction of the "Fosbury flop.")
6
.
. A blimp is initially at rest, hovering, when at t=0 the pilot turns on
the motor of the propeller. The motor cannot instantly get the propeller
going, but the propeller speeds up steadily. The steadily increasing force
between the air and the propeller is given by the equation F=kt, where k is a
constant. If the mass of the blimp is m, find its position as a function of
time. (Assume that during the period of time you're dealing with, the blimp
is not yet moving fast enough to cause a significant backward force due to
air resistance.)
7 S. A car is accelerating forward along a straight road. If the force of the
road on the car's wheels, pushing it forward, is a constant 3.0 kN, and the
car's mass is 1000 kg, then how long will the car take to go from 20 m/s to
50 m/s.
Problem 6.
SA solution is given in the back of the book.A difficult problem.
A computerized answer check is available.
.
A problem that requires calculus.
Homework Problems