Question

An irregularly shaped object 10 m long is placed with each end on a scale. If the scale on the right reads 96 N and the scale on the left reads 71 N, how far from the left is the center of gravity?
1. 5.7 m
2. 7.4 m
3. 4.3 m
4. 14m

Answer 1

Answer:

option 3, 4.3 m

Explanation:

In order to do this, we need to know some things.

First,  the object is not moving, therefore the net torque, about any point is zero.

Second, we have an upward force of 71 N from the left (Wl) and an upward force of 96 N from the right (Wr).

Third, the distance from the left end to the center of gravity is L (Length of the object) - distance of right end (I will call this value x): L - x

And fourth, as the torque is zero, the expression to use is the following:

T = Wr * x - Wl * (L - x) = 0

WrX = Wl (L - x)

Solving for x:

96x = 71(10 - x)

96x + 71x = 710

167x = 710

x = 4.25 or 4.3 m