Question

1. An elevator cab that weighs 27.8 kN moves upward. What is the tension in the cable if the cab’s speed is ___.

Find the mass of the elevator:

a. At rest

b. Uniform motion

c. Increasing at a rate of 1.2m/s2

d. Decreasing at the rate of 1.2m/s2

Please give me a solution and formula by letters. Thank you!

Answer 1

Given:

$W=27.8*10^3\:\rm N$

The tension in cable

$$T=W+ma$$

a. $a=0$

$$T=W=27.8\rm \: kN$$

b. $a=0$

$$T=W=27.8\rm \: kN$$

c. $a=1.2\:\rm m/s^2$

$$T=W+ma\\ =27.8\rm \: kN+\frac{27.8\rm \: kN}{9.8\:\rm N/kg}*1.2\:m/s^2=31200\:\rm N$$

d. $a=-1.2\:\rm m/s^2$

$$T=W+ma\\ =27.8\rm \: kN-\frac{27.8\rm \: kN}{9.8\:\rm N/kg}*1.2\:m/s^2=24396\:\rm N$$