How Much Work is Done by Gravity When Lowering a Piano with Two Ropes?

[talaroue]

Homework Statement

The two ropes are used to lower a 244.37 kg piano 9.47 m from a second-story window to the ground. How much work is done by gravity force? (T1=1805 N, q1=64°, T2=1112 N, q2=44°.)

How much work is done by T1 force?
How much work is done by T2 force?

Homework Equations

Wt1= mgdTcos(theata)

The Attempt at a Solution

Wt1= mdTcos(theata)=RIDICULOUSLY HUGE and wrong lol. What is wrong with the way I am approaching this problem?

 

[dx]

The force on the piano due to gravity is just the weight. So the work done by gravity is (force)(distance moved in direction of force) = weight times the distance lowered.

 

[talaroue]

mmhmmm. I understand that part. But the main problem is the tension parts

 

[dx]

Oh sorry, I didn't see there were two more parts to the question.

 

[talaroue]

I am sorry, I mean the work done by the first rope. I was thinking tension in my head. I thought the equation i came up with is right? What is wrong with it?

 

[dx]

The vertical component of T₁ is T₁sin(θ), not T₁cos(θ). You will also need to add a minus sign because the direction of displacement is opposite to this vertical component. So the work done by T₁ will be -dT₁sin(θ) (force times displacement in direction of force).

 

[talaroue]

so the equation i should be using is Wt1=-d*sin(theata)*T

isn't T the force?

 

[dx]

What is d? Isn't it the displacement?

 

[talaroue]

Yep! I got it thanks for the help I got it right but more importantly undersand where the anwser came from.