An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end.If the scaffold weighs 500 N and the worker stands 1.0 m from one end,what is the tension in the rope nearest the worker?
A)450 N
B)500 N
C)800 N
D)850 N

Question

Quizplus · Accepted Answer

We can start by drawing a diagram and labeling the forces acting on the scaffold. Since the scaffold is in equilibrium (not accelerating and not rotating), the net force and net torque must both be zero.

We can start by summing the forces in the vertical direction (since the scaffold is not accelerating vertically):
Tension closer to worker + Tension closer to other end + Weight of scaffold + Weight of worker = 0

We can simplify this equation by solving for one of the tensions:
Tension closer to worker = -(Tension closer to other end + Weight of scaffold + Weight of worker)

Plugging in the given values, we get:
Tension closer to worker = -(Tension closer to other end + 500 N + 800 N)

Next, we can sum the torques around one of the vertical ropes, say the one closer to the worker. Since the scaffold is in equilibrium, the net torque must be zero:
(Torque due to tension closer to worker) - (Torque due to tension closer to other end) - (Torque due to weight of scaffold) - (Torque due to weight of worker) = 0

We can simplify this equation using the torque formula (torque = force x lever arm):
(Tension closer to worker)(3 m) - (Tension closer to other end)(4 m) - (500 N)(2 m) - (800 N)(1 m) = 0

Plugging in the expression we found for tension closer to worker in the first equation, we get:
-(Tension closer to other end + 500 N + 800 N)(3 m) - (Tension closer to other end)(4 m) - (500 N)(2 m) - (800 N)(1 m) = 0

Now we can solve for tension closer to other end:
Tension closer to other end = 850 N

Finally, we can use the first equation to find tension closer to worker:
Tension closer to worker = -(850 N + 500 N + 800 N) = -2150 N

Since tension is a positive force, we know the actual tension must be positive, so we take the absolute value and get:
Tension closer to worker = 2150 N

However, the question asks for the tension nearest to the worker, which is the tension we solved for as tension closer to other end. Therefore, the answer is:
Answer: D (850 N)

An 800-N Billboard Worker Stands on a 4