Question

An elevator accelerates upwards at an acceleration of 2 m/s. The mass of the elevator is 3500 kg. What is the tension in the elevator cable?
A. 3500 N
B. 41,335 N
C. 16,823 N
D. 10,091 N

Answer 1

Answer:

B) 41,335 N

Explanation:

As the elevator moves upward the formula for the calculation of tension in the cable is given by.

                             T-mg =ma

                             T=mg+ma

                             T=3500*9.81+3500*2

                               =34335+7000

                             T=41,335 N

Answer 2

Answer:

The correct answer is B.

Explanation:

On the cable, there are two forces that produce the tension of the cable. One force is acceleration and the other is gravity.

First, we must calculate the force exerted by gravity on the elevator:

$F_{g}$ = m * g

$F_{g}$ =3500 kg * 9.81 $\frac{m}{s^{2} }$

$F_{g}$ = 34335 N

Now we calculate the force exerted by acceleration on the cable:

$F_{a}$ = m * a

$F_{a}$ = 3500 kg * 2 $\frac{m}{s^{2} }$

$F_{a}$ =7000 N

Finally, we add both forces and thus calculate the tension of the cable because:

∑$F_{y}$ = T - $F_{g}$ = m * a = $F_{a}$

T= $F_{g}$ + $F_{a}$

T= 34335 N + 7000 N

T= 41335 N

Have a nice day!