Question

A cart loaded with bricks has a total mass of 20.4 kg and is pulled at constant speed by a rope. The rope is inclined at 26.1 ◦ above the horizontal and the cart moves 20.1 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.6 . The acceleration of gravity is 9.8 m/s 2 . What is the normal force exerted on the cart by the floor? Answer in units of N.

Answer 1

Normal force, N = 154.5 N

Step-by-step explanation:

Given that,

Total mass of the cart, m = 20.4 kg

Angle of inclination,
`\theta=26.1^(\circ)`

Distance moved, d = 20.1 m

The coefficient of kinetic friction between ground and cart is 0.6

The value of acceleration due to gravity,
`g=9.8\ m/s^2`

Let N is the normal force exerted on the cart by the floor. It is given by :

`N=mg-T\ sin\theta`

`T\ cos\theta=\mu N`

`T\ cos\theta=\mu (mg-T\ sin\theta)`

`T\ cos(26.1)=0.6 (20.4* 9.8-T\ sin(26.1))`

T = 103.23 N

So, the normal force is :

`N=20.4* 9.8-103.23\ sin(26.1)`

N = 154.5 N

So, the normal force exerted on the cart by the floor is 154.5 N. Hence, this is the required solution.