physics problem help

Question

A meter stick is supported by a clamp at the 50 cm mark. A 40 g mass is placed at the 20 cm mark and a 60 g mass is placed at the 80 cm mark. How far from the 0-cm mark should a 30 g mass be placed to balance the stick?

a. 20 cm

b. 25 cm

c. 30 cm

d. 70 cm

Answer 1

For the meter stick to be balanced, the net torque should be zero. We get the magnitude of torque by multiplying the force acting on the lever arms by the distance from the fulcrum (balance) that these forces act on. In this case, the clamp at the 50 cm mark is our fulcrum.

The 40 g mass is placed 30 cm to the left of the fulcrum

The 60 g mass is placed 30 cm to the right of the fulcrum

Our equation for finding a net torque of zero is:

(30 g) * (9.8 m/s²) * (x) + (40 g) * (9.8 m/s²) * (-30 cm) + (60 g) * (9.8 m/s²) *(+30 cm) = 0

Where a negative distance represents being to the left of the fulcrum, and a positive distance represents being to the right of the fulcrum, and x is the distance we are solving for.

Solving for x algebraically, we find x = -20 cm, which is 20 cm to the left of the fulcrum (the 50 cm mark) and therefore is 30 cm from the 0-cm mark on the meter stick.