Question

A 2500-kg car is being pushed up a hill at an angle of 35 degrees. Determine the gravitational

force pulling down on the car if it is accelerating up the hill at a rate of 5 m/s/s.

Answer 1

The force that pulls the car down is Wₓ = 14052.6 N and the one that pushes the car up is F = 26552.6 N

Step-by-step explanation:

For this exercise we will use Newton's second law, let's set a reference system where the x axis is parallel to the plane, in the adjoint we can see the forces in the system.

sin 35 = Wₓ / W

cos 35 = W_y / W

Wₓ = W sin 35

W_y = W cos 35

Wₓ = 2500 9.8 sin 35

Wₓ = 14052.6 N

let's write the equations for each axis

and

Y axis

N-W_y = 0

N = W_y

X axis

F -Wₓ = m a

F = Wₓ + m a = mg sin 35 + m a

F = m (a + g sin 35)

let's calculate

F = 2500 (5 + 9.8 sin 35)

F = 26552.6 N

The force that pulls the car down is Wₓ = 14052.6 N and the one that pushes the car up is F = 26552.6 N