A 5-kg block is suspended by a rope from the ceiling of an elevator accelerates downward at 3.0 m/s². The tension force of the rope on the block is: A) 15 N, up B) 34 N, up C) 34 N, down D) 64 N, up E) 64 N, down

Question

Quizplus · Accepted Answer

The tension force in the rope can be found by analyzing the forces on the block. There are two forces acting on the block: the force due to gravity (weight) of 5g = 5 x 9.81 = 49.05 N, acting downward, and the tension force in the rope, acting upward. 
When the elevator accelerates downward, the tension force decreases, because the net force on the block is in the same direction as the force due to gravity. 
Using Newton's second law, F_net = ma, where F_net is the net force on the block, m is the mass of the block, and a is the acceleration of the block, we can find the tension force: 
F_net = T - mg = ma 
T = ma + mg = m(a + g) 
T = 5(3 + 9.81) = 54.05 N 
Since the acceleration is downward, the tension force is acting downward as well, so the answer is C) 34 N, down.

A 5-Kg Block Is Suspended by a Rope from the Ceiling