- Question 1: A small car and a large
truck are pushing against each other with their front ends. The truck
moves forward, while the car is forced to move backwards. Is the force
with which the truck pushes the car greater or equal to the force of
the car on the truck? In either case, explain what is happening.
Answer: The two forces are equal, as stated in Newton's
third law. The reason the car is able to push the car back is that
its weight
is greater than that of the car, so the maximum force of friction between
its tires and the ground is also greater (friction with the ground
is what makes a car/truck move forward).
- Question 2: Suppose you drop a ball from a tall
building, and air resistance can be neglected, so that the only force
acting on the ball as it falls is gravity. While it falls, is its mechanical
energy conserved? Is its momentum conserved? For each of the two, give
a short explanation.
Answer: Mechanical energy is conserved, because the
only force acting on the ball is gravity, which is conservative (it
has a potential energy). Momentum is not conserved, because there is
a net external force acting on the ball (gravity): p = mv,
and v keeps
increasing!
- Question 3: Now take into account the fact that
air resistance acts on the ball. Is the mechanical energy of the ball
conserved? Is its momentum conserved? For each one, give a short explanation.
Answer: Mechanical energy is not conserved now, because
there is a non-conservatuve force acting on the ball (air resistance)
which does negative work on it, so mechanical energy decreases. Momentum
is still not conserved, for the same reason as before, although now
the net external force mg – Fair is
smaller, so air resistance is trying to keep the momentum constant.
- Question 4: A person is swinging a ball tied to
a string in a vertical circle at constant speed. Is the tension in
the string the same or different
when the ball is at different locations? Explain briefly.
Answer: The tension is different at different places.
It is greater at the bottom, where tension and gravity act in different directions
and tension has to overcome gravity plus provide the centripetal acceleration.
At the top, tension and gravity are in the same direction and gravity
helps provide the required centripetal force.
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