What is the tension of the cable? Physics problem help please?

Question

What is the tension in the cable on a 1.20 x 10 to the 3 kg elevator that is:

a. accelerating downward at a rate of 1.05 m/s/s

b. accelerating upward at a rate of 1.05 m/s/s

c. moving downward at a constant velocity of 1.10 m/s

Please explain how you get the answers. I'm really having a difficult time solving them. Thank you.

Answer 1

Hi,

The tension of the cable is a force that is upwards = T

Gravity is another force that is downwards = Fz

The second law of Newton says :   Ftotal = m. a

So here it is  T - Fz = m. a

a)  a = 1.05 m/s^2 downwards ==>

T - (m . g ) = m . (-1.05)     (a is downwards therefor negative)

==>  T = m ( - 1.05 + g)  = 1.2.10^3 . (-1.05 + 9.8) = 10500 N

b)  a = 1.05 m/s^2 upwards

T - (m.g) = m. (1.05)    (a is positive now because upwards)

==>  T = m (1.05 + g) = 1.2.10^3 . (1.05 + 9.8) = 13020 N

c)  constant velocity  ==>  a = 0 !!!!

so  T - (m.g) = m . 0  

==>  T = m.g = 1.2.10^3 . 9.8 = 11760 N