Question

You are given a four-wheeled cart of mass 15 kg, where the distance between a wheel and its nearest neighbors is 1.2 m. Suppose we load this cart with a crate of mass 102 kg, where the crate's center of mass is located in the back-middle of the cart, 0.300 m from its center.

(a) Find the weight on the nearer wheels of the cart under this load?
(b) Find the weight on the farther wheels of the cart under this load.

Answer 1

(a) The weight on the two nearer wheels combined is ‭323.73‬ N

(b) The weight on the two farther wheels combined is ‭824.04 N

Step-by-step explanation:

Here, we have

Taken the location of the four wheels as equidistant

The sum of moment at a point is equal to 0, that is ∑M = 0

Therefore, taking moment about the center of the cart with clockwise moments as positive and anticlockwise moments as negative, we have

2×Rw × 0.6 m + 102 × 0.3 × 9.81 - 2×Fw × 0.6 = 0

Where:

Rw = Rear wheel

Fw = Front wheel

Therefore, we have

1.2·Rw +‭300.186‬ = 1.2·Fw

1.2 Fw - 1.2 Rw = 300.186‬ N ....(1)

Also, ∑F = 0

That is 2·Rw + 2·Fw - 102×9.81 - 15 × 9.81 = 0

2·Rw + 2·Fw = ‭1,147.77‬ N............(2)

Placing Rw = (1.2 Fw - 300.186)/1.2 into equation 2 and solving, we obtain

Solving equations (1) and (2), we get

Rw = 161.865 N and Fw = 412.02 N

Therefore,

(a) The weight on the two nearer wheels is the weight on the Rw wheels given by

= 2 × 161.865 N = ‭323.73‬ N

(b) The weight on the farther wheels is the weight on the Fw wheels given by

= 2 × 412.02 N = ‭824.04 N.