A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip?
A)0 m
B)0.3 m
C)0.5 m
D)0.7 m
E)0.9 m

Question

A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip? 
A)0 m 
B)0.3 m 
C)0.5 m 
D)0.7 m 
E)0.9 m

Quizplus · Accepted Answer

In order for the plank to remain in equilibrium, the sum of the clockwise torques must equal the sum of the counterclockwise torques.

Taking moments about the left support:

(clockwise torque) = (counterclockwise torque)

(800N)(x) = (100N)(1.0m) + (plank weight)(5.0m) + (800N)(4.0m)

800x = 500 + 500 + 4000

800x = 5000

x = 6.25

Therefore, the person can stand no closer than 6.25 - 1.0 = 5.25 m from the left end of the plank. This is closer to the left end than to the right, so the answer is closest to Choice C, 0.5 m.

A Horizontal, 10-M Plank Weighs 100 N