Question

Whale an elevator of mass 877 kg moves downward, the tension in the supporting cable is a constant 7730 N. Between t = 0 and t = 4.00 s, the elevator's displacement is 5.00 m downward. What is the elevator's speed at t = 4.00 s?

Answer 1

3.22 m/s

Step-by-step explanation:

First, use Newton's second law to find the acceleration.

∑F = ma

T − mg = ma

7730 N − (877 kg) (9.8 m/s²) = (877 kg) a

a = -0.986 m/s²

Next, use a constant acceleration equation to find the final velocity.

Given:

Δy = -5.00 m

Δt = 4.00 s

a = -0.986 m/s²

Find: v

Δy = vt − ½ at²

-5.00 m = v (4.00 s) − ½ (-0.986 m/s²) (4.00 s)²

v = -3.22 m/s

The elevator's speed is 3.22 m/s.