An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5.0 kN, and the circle’s radius is 10 m. At the top of the circle, what are the (a) magnitude FB and (b) direction (up or down) of the force on the car from the boom if the car’s speed is ? What are (c) FB and (d) the direction if ?

Question

An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5.0 kN, and the circle’s radius is 10 m. At the top of the circle, what are the (a) magnitude FB and (b) direction (up or down) of the force on the car from the boom if the car’s speed is ? What are (c) FB and (d) the direction if ?

Answer 1

To determine the force on the car from the boom at the top of the circle, we need to consider the forces acting on the car.

(a) Magnitude of FB:
At the top of the circle, the net force acting on the car is the centripetal force required to keep the car moving in a circular path. This force is provided by the tension in the boom, FB. The centripetal force is given by the formula:

FC = m * v^2 / r

where m is the mass of the car and riders, v is the speed of the car, and r is the radius of the circle.

In this case, the weight of the car and riders is acting vertically downward, equal to their combined weight, which is 5.0 kN. At the top of the circle, the tension in the boom must counteract the weight, so the magnitude of FB is equal to the weight:

FB = 5.0 kN

(b) Direction (up or down) of FB:
The direction of FB depends on the orientation of the coordinate system. If we consider upward as the positive direction, then the force FB would be directed upward to counteract the downward weight. Therefore, the direction of FB is up.

(c) Magnitude of FB when v = 0:
When the speed of the car, v, is zero at the top of the circle, the tension in the boom must provide the entire centripetal force to keep the car in circular motion. The centripetal force is given by the formula mentioned earlier:

FC = m * v^2 / r

Since v is zero, the magnitude of FC is also zero. This means that the magnitude of FB must be equal to the weight of the car and riders:

FB = 5.0 kN

(d) Direction of FB when v = 0:
Since the weight of the car and riders is acting vertically downward, FB must act in the same direction to counteract it. Therefore, the direction of FB is down.