Question

A car moves horizontally with a constant acceleration of 3 m/s 2 . 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?

Answer 1

Answer:

The string make with the vertical an angle of 17.8°

Explanation:

The ball will move backwards until the horizontal component of its weight is accelerating it by 3 m/(s^2).

The horizontal component of its weight is calculated as follows

m*g*sinθ

The acceleration of the car is

m*a

a is the acceleration of the car (3 m/(s^2)), m is the mass of the ball, g is the gravitational acceleration (9. 81 m/(s^2)), and θ is the angle between the string and the vertical.

Notice that the ball doesn't swing, so the forces are at equilibrium, then:

m*g*sinθ = m*a

θ = arcsin(a/g)

θ = arcsin(3/9.81)

θ =  17.8 °

Answer 2

Here you need to draw a force system.

The car is the center and you have mainly two forces: velocity and gravity.

The angle they ask you for is the same angle formed by the velocity (mass* acceleration) and the gravity (mass*gravity)

And to know the angle you need to do the tangent.

Tg∡=$\frac{m*3m/s^{2} }{m*9.81m/s2}$

Both masses canceld and

Tg∡=$\frac{3m/s^{2} }{9.81m/s2}$

∡=arcTg 0.30

∡=187.35°