2. (20 pts)
a) (5 pts) In what direction is the force exerted on a planet orbiting the sun? (You may assume that the
orbit is circular.)
Towards the sun.
b) (5 pts) In order for a car to turn a corner, there must be a force acting on the car in the direction of
the turn. Usually, friction provides this force. In a situation where there is very little friction, what
else could be done to help provide the necessary force? And how does this help provide a force in the
correct direction?
The turn could be banked. Then the force exerted on the car by the road is not vertical but pointed
inward a bit. The inward part of this force is what causes the car to make the turn.
c) (5 pts) A roller-coaster passes through the highest point of the track at the top of a loop. The
passengers feel (momentarily) weightless. Since they are still moving in a circle, there must be a
downward force. (i) What is causing this force and (ii) why do they not feel the car seat pressing
against them? (This would eliminate the sensation of weightlessness.)
(i) The downward force on the passengers is their weight, caused by gravitational attraction with the
earth.
(ii) They feel “weightless” because the force of gravity is enough to keep them moving in a circle without
additional force from the car seat.
d) (5 pts) Which would require more force, swinging the rubber chicken in a circle of 1 m radius at
5 m/s or in a circle of 2 m radius at 5 m/s?
Since the speeds are the same, moving in a circle of smaller radius requires more force.