# Calculating Work: Lowering a Piano with Two Ropes

• sktgurl930
In summary, the two ropes are used to lower a 267.18 kg piano 5.34 m from a second-story window to the ground. When calculating the work done by gravity, the equation W=Fd is used, resulting in 13982.004 J. However, when calculating the work done by T1 and T2 forces, the equation W=FdCos(angle) must be used, taking into account the angle between the rope and the direction of movement. This results in a negative value of -9618.56 J for T1 and an unknown value for T2.
sktgurl930

## Homework Statement

The two ropes are used to lower a 267.18 kg piano 5.34 m from a second-story window to the ground. How much work is done by gravity force? (T1=1864 N, θ1=64°, T2=1231 N, θ2=50°.)
How much work is done by T1 force?
How much work is done by T2 force?

W=Fd
W=FdCos(angle)

## The Attempt at a Solution

the first part worked out fine i had gotten
13982.004 J

but when I tired the second I got it wrong cause i did
W=FdCos(angle) and then subtracted it from the answer in the first part
-9618.56 J

and for the third part I just used
the equation
W=Fdcos(angle)

sktgurl930 said:
but when I tired the second I got it wrong cause i did
W=FdCos(angle) and then subtracted it from the answer in the first part
-9618.56 J

Don't subtract the answer from the work done by gravity, just calculate W=FdCos(angle) for the answer.

and for the third part I just used
the equation
W=Fdcos(angle)

Yes, do it that way for both T1 and T2.

I try but it doesn't work out
am i missing something?
is it positive or negative ?? i was thinking its negative goes its going down

Yes, since the rope tension act against the direction of motion the work would be negative.

You need to use the angle between the rope and the direction of movement. You don't simply use 64 and 50 degrees, just because those are the numbers you see in the figure or problem statement.

thank u
it makes sense now

## 1. How do you calculate the work done when lowering a piano with two ropes?

The work done when lowering a piano with two ropes can be calculated using the formula W = F x d, where W is the work done, F is the force applied, and d is the distance over which the force is applied. In this case, the force is the weight of the piano and the distance is the height the piano is lowered.

## 2. What is the difference between work and force in this scenario?

In this scenario, force refers to the weight of the piano, which is the amount of downward force exerted by the piano. Work, on the other hand, is the measure of the energy required to move the piano while overcoming this downward force.

## 3. Is the work done when lowering a piano with two ropes the same as when using one rope?

No, the work done when using two ropes to lower a piano will be less compared to using one rope. This is because with two ropes, the weight of the piano is distributed between the two ropes, resulting in less force required to lower it.

## 4. How does the angle of the ropes affect the work done?

The angle of the ropes can affect the work done when lowering a piano. The steeper the angle of the ropes, the more force will be required to hold the piano in place. This will result in more work being done to lower the piano.

## 5. Can you calculate the work done if the weight of the piano is unknown?

No, in order to calculate the work done when lowering a piano with two ropes, you need to know the weight of the piano. Without this information, it is not possible to accurately determine the work done.

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