# Work Done by T1 and T2 in Lowering a Piano

• ChrisMC
In summary, the conversation is about finding the work done by the three forces (W, T1, T2) while lowering a 235 kg piano from a second-story window to the ground. T1 is 45 degrees north of east and T2 is 60 degrees north of west. Using the work equation W = fd cosθ, the work done by T1 was calculated to be 4316.886899 J and the work done by T2 was calculated to be 8668.914292 J. However, the correct values for T1 and T2 are given as 1820 N and 1120 N, respectively. To find the work done by each force, the angle between the displacement vector and the
ChrisMC
The two ropes seen in Figure Ex11.9 are used to lower a 235 kg piano 5.5 m from a second-story window to the ground. How much work is done by each of the three forces? (T1 = 1820 N andT2 = 1110 N)

t1 is 45degrees north of east
t2 is 60degrees north of west

w = J
T1 = J
T2 = J

w=fd

I got work done by weight to be 12666.5j which is correct, how do i find the tensions?

To get help, you need to show Figure Ex11.9. You have it, but we don't.

Assuming that the piano is lowered at constant speed (as is usually the case with pianos being moved), what is the net force acting on the piano?

0? but its looking for work

Zero is correct. Although the net force does zero work and the net work done on the piano is zero, the individual forces acting on the piano do do work. The sum of all the works done by all the forces (i.e. the net work) must be zero.

First things first. How did you calculate the works done by T1 and T2? Please show what equation you used and what numbers you put in.

Those are the ones i need to figure out, i figured out the force in the y direction with trig functions then used w=fd

I got t1 = 4316.886899
t2 = 8668.914292

but they were wrong

ChrisMC said:
Those are the ones i need to figure out, i figured out the force in the y direction with trig functions then used w=fd

I got t1 = 4316.886899
t2 = 8668.914292

but they were wrong
I asked you to show what equation you used and what numbers you put in. You say W = Fd, OK. What numbers did you put in W = fd to get t1 = 4316.886899 and t2 = 8668.914292 ?

By the way, lose the extra significant figures. You don't need more than three.

to get t1 I used w= (1100*sin45)*5.5
to get t2 I used w= (1820*sin60)*5.5

*If I don't keep the sigfigs the webquestions get counted wrong

ChrisMC said:
to get t1 I used w= (1100*sin45)*5.5
to get t2 I used w= (1820*sin60)*5.5

*If I don't keep the sigfigs the webquestions get counted wrong
You mean "to get w1 and w2" because t1 and t2 are given. Minor mistake. The most serious mistake is in you application of the work equation.

The work done by a constant force is W = f d cosθ, where θ is the angle between the displacement vector and the force. Since the displacement vector is down, and t1 is 60o above the horizontal, what is the angle between the displacement and the t1? How about t2?

I have no idea, what that means t1s angle 150? t2s 135?

Correct. So what are the cosines of 150o and 135o? You can put it together now.

cos(135) = -sqrt(2)/2 and cos(150) = -sqrt(3)/2

Where do I plug them into? what would be the equation to find T1?

Are you looking for T1? Look at your initial posting. It says T1 = 1820 N and T2 = 1120 N. You are looking for the work done by T1 and T2. As I said before, the work done by each force is F d cosθ. Just put it together.

## 1. What is meant by "work done" in the context of lowering a piano?

Work done refers to the amount of energy expended or force applied in order to lower a piano from a higher position to a lower position.

## 2. Why is it important to consider the work done when lowering a piano?

Considering the work done allows us to understand the amount of energy needed to safely and effectively lower a piano without causing damage or injury to the people involved.

## 3. How is the work done calculated when lowering a piano?

The work done is calculated by multiplying the force applied to the piano by the distance it is lowered. This is expressed in units of joules.

## 4. What factors can affect the work done when lowering a piano?

The weight of the piano, the distance it is lowered, and the force applied are the main factors that can affect the work done. Other factors such as friction and the angle at which the piano is lowered can also play a role.

## 5. What are some safety precautions to keep in mind when lowering a piano?

Some safety precautions to keep in mind when lowering a piano include using proper equipment such as pulleys and straps, having enough people to help with the task, and ensuring the area is clear of any obstacles. It is also important to communicate and plan the lowering process beforehand to avoid accidents.

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