Question

part 2: an elevator is moving down with a constant speed. inside the elevator, there is a block of mass m hanging from a rope with length x₁. the elevator then gradually slows to a stop with constant acceleration. image of elevator with hanging block 1. which statement is true when the elevator is moving down and gradually slowing down? a. the block has an upward acceleration. b. the block has a downward acceleration. c. the block has an acceleration of 0. d. the acceleration of the block keeps changing directions. 2. which of the following is true about the tension force on the rope connected with the block when the elevator is gradually slowing down? a. t > mg b. t = mg c. t < mg d. t = 0

Explanation:

Question 1

When the elevator is moving down and slowing down, its velocity is downward but decreasing. Acceleration is the rate of change of velocity. Since the velocity is decreasing in the downward direction, the acceleration must be in the opposite direction (upward) to slow it down. The block moves with the elevator, so it has the same acceleration as the elevator.

For the block, we use Newton's second law \( F_{net}=ma \). The forces on the block are tension \( T \) upward and weight \( mg \) downward. The net force \( F_{net}=T - mg \). From question 1, we know the acceleration \( a \) is upward (positive if we take upward as positive). So \( T - mg=ma \) (since \( a>0 \) upward). Rearranging, \( T = mg + ma \), which means \( T>mg \).

Answer:

a. The block has an upward acceleration.

Question 2