Question

You are pushing a 5.15kg box toward the right over rough grass. If the magnitude of your push is 37.1 N, and the coefficient of kinetic friction with the grass is 0.350, what will be the magnitude and direction of the acceleration of the box?

Answer 1

On pushing the box towards right the force(F) applied is in right direction and force of friction(f) will opposite to it i.e. in left direction,

Given

Mass of block (m) = 5.15 kg

Coefficient of kinetic friction (μ) = 0.350

Force of friction (f) = μmg

f = 0.350×5.15×9.8 = 17.66 N towards left

Force of push (F) = 37.1 N towards right

The net force on box Fnet = 37.1 – 17.66 = 19.44 N towards right

Net force on the block will be equal to mass times acceleration(a).

i.e.

Fnet = m×a = 5.15 a

5.15 a = 19.44

a = 19.44/5.15 = 3.77 m/s^2 towards right.

The acceleration of block will be 3.77 m/s^{​​​​​​2} in magnitude and in the right direction.