Sample Problem Force And Motion 11

Sample Problem Force And Motion 11

Even some seasoned roller-coaster riders blanch at the thought of riding the Rotor, which is essentially a large, hollow cylinder that is rotated rapidly around its central axis ). Before the ride begins, a rider enters the cylinder through a door on the side and stands on a floor, up against a canvas-covered wall.

SOLUTION: We start with a question: What force can keep the rider from falling and how is it related to the speed v of her and the cylinder? To answer, we use three Key Ideas:

1. The gravitational force  on the rider tends to slide her down the wall, but she does not move because a frictional force from the acts upward on her .

2. If she is to be on the verge of sliding down, that upward force must be a static frictional force at its maximum value,  here N is the magnitude of the normal force N on her from the cylinder .

3. This normal force is directed horizontally toward the central axis of the cylinder and is the centripetal force that causes the rider.

A Rotor in an amusement park, showing the forces on a rider. TIle centripetal force is the normal force with which the wall pushes inward on the rider.
A Rotor in an amusement park,
showing the forces on a rider. TIle centripetal force is the normal
force with which the wall pushes inward on the rider.

Substituting for N and then solving for Y, we find

1

If the rider’s mass is 49 kg, what is the magnitude of the centripetal force on her?

SOLUTION: According to

1

Although this force is directed toward the central axis, the rider has an overwhelming sensation that the force pinning her against the wall is directed radially outward.

CHECKPO’NT 5: If the Rotor initially moves at the minimum required speed for the rider not to fall and then its speed is increased in steps, do the following increase, decrease, or main  he same: (a) the magnitude o (b) the magnitude.of N  (c) the value.

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