How Do You Calculate Cable Tension and Power in an Inclined Plane Scenario?

[davekardle]

Homework Statement

What's the tension on each cable ? and the power required to overcome tension (?)
Here's the diagram:
http://en.wikipedia.org/wiki/File:Planincline-schema.JPG

Homework Equations

F=Vsin(theta) ( constant velocity ) = a= 0
Inclined (24.25 degrees) to the horizontal plane)
Weight of block: 25T lighter then the counterweight when pushed upwards.
and 25T heavier when pushed downwards the inclined plane.

Ascending and descending journey time: 4 min
vertical height: 55m
Average velocity calculated:

Inclined displacement = 55M/ sin(24.25)

Average velocity= (55m/sin(24.25))/2(60)s = 1.11 m/s on each journey upwards and downwards. ( is this right ? ) should it be divided by 4(60) instead?

The Attempt at a Solution

F(push) = (25 x 10^3)(9.81)sin(24.25)
F(counterweight) = (50 x 10^3)(9.81)sin(24.25)

Tension on cables: ((50 x 10^3)(9.81)sin(24.25)) - (25 x 10^3)(9.81)sin(24.25)

The block is attached to the counterweight by two groups of 14 cables
so is the tension on each group of cable = T= Total tension/2 = 50.350KN

The power required to lift the block on each group of cable

Work done = Tension x displacement
Work done= 50.350 KN x 134m
Work done= 6747.0 KN.m
Work = 6747.0 KN.m/2(60) = 56.2 KW for each group of 14 cables.

is this calculations correct ?

 

[pongo38]

"so is the tension on each group of cable = T= Total tension/2 = 50.350KN "
What do you think? Can you compare this with anything else you know, in order to verify its rough value?
You could ask/answer the same question in relation to power. What does 56 kW "look like"? Can you compare it with anything else you know, such as a car, a horse, or a kettle, say?