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 vertical is:
A)0°
B)1.4°
C)24°
D)90°
E)cannot be found without knowing the mass of the ball

Question

Quizplus · Accepted Answer

The gravitational force acting on the ball is always directed vertically downwards. Therefore, in order for the ball to move along with the car as it rounds the curve, there must be an additional force acting on the ball towards the center of the curve. This force is provided by the tension in the string.

Since the car is moving at a constant speed, the net force acting on the ball in the horizontal direction must be zero. Therefore, the tension in the string must provide the centripetal force necessary to keep the ball moving in a circle. Using centripetal force formula F = mv^2/r, we can find the tension in the string.

F = mv^2/r
T = m*v^2/r

We do not need to know the mass of the ball to find the angle between the string and the vertical because it will cancel out in the calculation. Therefore,

tanθ = (T/mg)
tanθ = v^2/(rg)
tanθ = (18 m/s)^2 / (75 m * 9.81 m/s^2)

tanθ = 0.239
θ = 13.8°

However, this angle is the angle between the string and the horizontal. Since the string is also under the influence of gravity, we need to add the angle between the horizontal and the vertical (90°) to get the angle between the string and the vertical.

θ = 13.8° + 90° = 103.8° ≈ 104°

Therefore, the answer is C) 24°.

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