An object is observed to be moving at constant speed in a
certain direction. Can you conclude that no forces are acting on it?
Explain. [Based on a problem by Serway and Faughn.]
A car is normally capable of an acceleration of 3 m/s2. 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.]
(a) Let T be the maximum tension that the elevator's cable can
withstand 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. ("Interpret" means
to analyze the behavior of the equation, and connect that to reality,
as in the self-check on page 139.)
A helicopter of mass m is taking off vertically. The only forces
acting on it are the earth's gravitational force and the force, Fair,
of the air pushing up on the propeller blades.
(a) If the helicopter lifts off at t = 0, what is its vertical speed at
(b) Plug numbers into your equation from part a, using m = 2300
kg, Fair = 27000 N, and t = 4.0 s.
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/s2. Suppose a high-jumper has a mass of
(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
(Actually, the reason for the big change between '64 and '68 was the
introduction of the "Fosbury flop.") ?
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
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?
Solution, p. 279
Some garden shears are like a pair of scissors: one sharp blade
slices past another. In the "anvil" type, however, a sharp blade
presses against a flat one rather than going past it. A gardening
book says that for people who are not very physically strong, the
anvil type can make it easier to cut tough branches, because it
concentrates the force on one side. Evaluate this claim based on
Newton's laws. [Hint: Consider the forces acting on the branch,
and the motion of the branch.]
A uranium atom deep in the earth spits out an alpha particle.
An alpha particle is a fragment of an atom. This alpha particle has
initial speed v, and travels a distance d before stopping in the earth.
(a) Find the force, F, that acted on the particle, in terms of v, d,
and its mass, m. Don't plug in any numbers yet. Assume that the
force was constant.
(b) Show that your answer has the right units.
(c) Discuss how your answer to part a depends on all three variables,
and show that it makes sense. That is, for each variable, discuss
what would happen to the result if you changed it while keeping the
other two variables constant. Would a bigger value give a smaller
result, or a bigger result? Once you've figured out this mathematical
relationship, show that it makes sense physically.
(d) Evaluate your result for m = 6.7×10-27 kg, v = 2.0×104 km/s,
and d = 0.71 mm. p
You are given a large sealed box, and are not allowed to open
it. Which of the following experiments measure its mass, and which
measure its weight?
(a) Put it on a frozen lake, throw a rock at it, and see how fast it
scoots away after being hit.
(b) Drop it from a third-floor balcony, and measure how loud the
sound is when it hits the ground.
(c) As shown in the figure, connect it with a spring to the wall, and
watch it vibrate. [Hint: Which experiments would give different
results on the moon?]
While escaping from the palace of the evil Martian emperor,
Sally Spacehound jumps from a tower of height h down to the
ground. Ordinarily the fall would be fatal, but she fires her blaster
rifle straight down, producing an upward force FB. This force is insufficient
to levitate her, but it does cancel out some of the force of
gravity. During the time t that she is falling, Sally is unfortunately
exposed to fire from the emperor's minions, and can't dodge their
shots. Let m be her mass, and g the strength of gravity on Mars.
(a) Find the time t in terms of the other variables.
(b) For sufficiently large values of FB, your answer to part a becomes
nonsense - explain what's going on.
Rockets work by pushing exhaust gases out the back. Newton's third law
says that if the rocket exerts a backward force on the gases, the gases
must make an equal forward force on the rocket. Rocket engines can
function above the atmosphere, unlike propellers and jets, which work by
pushing against the surrounding air.