Question

Your shopping cart has a mass of 65 kilograms.In order to accelerate the shopping cart down an aisle at 0.30 m/s^2, what Force would you need to use or apply to the cart assuming the coefficient of friction between the cart and the floor is 0.01?

Answer 1

25.88 N

Step-by-step explanation:

Mass of the shopping cart,
`m=65 kg`

The coefficient of friction between the cart and the floor,
`\mu= 0.01`

Let, F be the required force to accelerate the cart at
`a=0.30 m/s^2`.

Gravitational force, mg, acts downward which is being balanced by the normal reaction, N, on the cart by the floor.

As the motion of the cart in the vertical direction is zero. So, using the static equilibrium condition will be zero.

From free body diagram (FBD):

`N-mg=0`

`\Rightarrow N=mg.`

the net force action in this direction The frictional force, f, acts in the direction to opposes the motion of the cart as shown.

`f=\muN=\mu mg`

Now, apply the dynamic equilibrium condition in the horizontal direction, i.e. net force acting on the body equals the rate of change of momentum of the body. From the FBD of the cart, we have

`F-f-ma=0`

`\Rightarrow F=f+ma`

`\Rightarrow F=\mu mg+ma`

`\Rightarrow F=m(\mu g +a)`

`\Rightarrow F=65(0.01* 9.81 + 0.3)`

`\Rightarrow F=25.88 N.`

Hence, 25.88 N force required to accelerate the body with 0.03
`m/s^2` .