A car moves horizontally with a constant acceleration of 3 m/s². A ball is suspended by a string from the ceiling of the car; the ball does not swing, being at rest with respect to the car. What angle does the string make with the vertical? A) 17 B) 35 C) 52 D) 73 E) Cannot be found without knowing the length of the string

Question

Quizplus · Accepted Answer

The tension in the string can be resolved into two components: one vertical and one horizontal. The vertical component supports the weight of the ball, while the horizontal component causes the ball to accelerate horizontally with the same acceleration as the car.

Since the ball remains at rest with respect to the car, the vertical component of tension must exactly counteract the weight of the ball. Therefore, the vertical component of tension is equal to mg, where m is the mass of the ball and g is the acceleration due to gravity.

The horizontal component of tension is equal to ma, where a is the horizontal acceleration of the car and the ball.

Since the string must be at an angle to provide both a horizontal and vertical component of tension, we can use trigonometry to find the angle.

tan(theta) = (horizontal component of tension)/(vertical component of tension)
tan(theta) = (ma)/(mg)
tan(theta) = a/g
tan(theta) = 3/9.81

Solving for theta:
theta = tan^-1(3/9.81)
theta ≈ 17°

Therefore, the angle that the string makes with the vertical is approximately 17°.

A Car Moves Horizontally with a Constant Acceleration of 3