A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the verticle is:
A) 0
B) 1.4°
C) 24°
D) 90°
E) cannot be found without knnowing the mass of the ball

Question

Quizplus · Accepted Answer

The force acting on the ball is the tension in the string, which is always directed towards the center of the circular path. In this case, the center of the circle is below the ball, and so the tension force also has a vertical component, which is equal and opposite to the force of gravity.

Since the car is moving at a constant speed, the net force on the ball must be zero, and so the vertical component of the tension force must exactly balance the force of gravity. Therefore, the angle between the string and the vertical must be equal to the angle whose tangent is the ratio of these two forces:

tan θ = (mg) / (mv² / r)

where m is the mass of the ball, g is the acceleration due to gravity, v is the speed of the car, and r is the radius of the circular path.

Since we are not given the mass of the ball, we cannot calculate this angle exactly. However, we can make an estimate by assuming that the mass of the ball is relatively small compared to the other quantities, and so the term (mg) can be neglected. Under this assumption, we have:

tan θ ≈ 0.2

which gives:

θ ≈ 11.5°

This is closest to choice C, 24°, but it is not an exact match. Therefore, we should choose C as the best answer, but with the caveat that it is only an estimate.

A Car Rounds a 75-M Radius Curve at a Constant