Question

A cable lowers a 1150 kg elevator so that the elevator's speed increases from zero to 4.0 m/s in a vertical distance of 6.4 m What is the force that the cable exerts on the elevator while lowering it? (Assume that the system is the elevator and Earth.) Express your answer to two significant figures and include the appropriate units. What is the force that the cable exerts on the elevator while lowering it? (Assume that the system is the elevator only.) Express your answer to two significant figures and include the appropriate units.

Answer 1

From the given data, the elevator moving downward with a velocity 4.0 m/s from a height 6.4 m. Hence, the downward acceleration of the elevator is as follows: 12 – u? = 2ah v2-u? 2h (4.0 m/s)? - (0 m/s) 206.4 m) =1.25 m/s? Part A (Elevator and Earth) Calculate the force exerted by the cable on the elevator as follows: The force exerted by the cable on the elevator is upward and the weight acting downward.

From the Newton's 2nd law of motion, the force exerted by the cable on the elevator is as follows: mg - FCon El = ma FCon El = mg - ma = (1150 kg)(9.8 m/s2 - 1.25 m/s?) = 9.8325 N - 9.810' N Part B (Elevator) Calculate the force exerted by the cable on the elevator as follows: In the frame of elevator system, the acceleration of the elevator is still 1.25 m/s. The acceleration of the elevator doesn't depend on the system. Hence, the force exerted by the cable on the elevator is as follows: mg - FC on E1 = ma FCon El = mg - ma =(1150 kg)(9.8 m/s² -1.25 m/s²) =9.8325 N - 9.8x10² N