Question

Mary applies a force of 79 N to push a box with an acceleration of 0.45 m/s2. When she increases the pushing force to 84 N, the box's acceleration changes to 0.61 m/s2. There is a constant friction force present between the floor and the box. slader

Answer 1

The mass of the box, m = 31.25 kg

Step-by-step explanation:

It is given that,

Condition (1)

Force applied by Mary, F₁ = 79 N

Acceleration of the box,
`a_1=0.45\ m/s^2`

Condition (2) :

Force applied by Mary, F₂ = 84 N

Acceleration of the box,
`a_2=0.61\ m/s^2`

Let m is the mass of the box. It is assumed to find the mass of the box. The resultant forces acting on the box in condition (1) are :

`79-f=m* 0.45`...........(1)

f is the force of friction acting between the floor and the box.

The resultant forces acting on the box in condition (2) are :

`84-f=m* 0.61`..........(2)

On solving equation (1) and (2) we get :

f = 64.938 N

m = 31.25 kg

So, the mass of the box is 31.25 kg. Hence, this is the required solution.