Work and Tension Problem

In summary, a 255kg piano is being lowered 5.0m from a second-story window to the ground using two ropes. The first rope, T1, has a force of 1830N and an angle of 60∘pointing to the upper left, while the second rope, T2, has a force of 1295N and an angle of 45∘pointing to the upper right corner. The downward force, w, has a force of 2500N. The work done by each of the three forces is as follows: T1 = -7920J, T2 = -4580J, and w = -12500J. To find the work for each force
  • #1
wind326
1
0
Two ropes are used to lower a 255kg piano 5.0m from a second-story window to the ground. How much work is done by each of the 3 forces? T1 is 1830 N with angle of 60∘pointing to the upper left, T2 is 1295N and has angle of 45∘and pointing to the upper right corner. The w is pointing downwards with a force of 2500N.

The answers are: T1= -7920J and T2 = -4580J

I understand how to find the work for the downward force, it is 12500J, but i`m not certain about the other two tensions. Please help if you can!

My calculation for T1 was:
T1 = -12500J + [(1830N cos 60)(5.0m)]
= -7925 J
 
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  • #2
Just use th same. Work=Integral(F.dx) where dx is the interval you're moving. If the force is constant, then Work=F*x. Just split the forces in x and in y and calculate the work in each direction for each of the forces you want. Good luck!
 
  • #3


My calculation for T2 was:
T2 = -12500J + [(1295N cos 45)(5.0m)]
= -4580J

I would say that your calculations for T1 and T2 are correct. The work done by each force can be calculated using the formula W = Fd, where W is work, F is force, and d is distance. In this case, the distance is 5.0m for both ropes.

For T1, we can use the given force of 1830N and the angle of 60 degrees to find the horizontal component of the force, which is 1830N cos 60 = 915N. This horizontal component is the force that is doing the work of pulling the piano horizontally. Multiplying this by the distance of 5.0m gives us 915N x 5.0m = 4575J. However, since the force is pointing in the opposite direction of the displacement, the work done by T1 is -4575J. This is why your calculation for T1 is correct.

For T2, we can use the given force of 1295N and the angle of 45 degrees to find the horizontal component of the force, which is 1295N cos 45 = 915N. This horizontal component is also the force that is doing the work of pulling the piano horizontally. Multiplying this by the distance of 5.0m gives us 915N x 5.0m = 4575J. However, since the force is pointing in the opposite direction of the displacement, the work done by T2 is also -4575J. This is why your calculation for T2 is correct.

Overall, the work done by each force can be determined by finding the horizontal component of the force and multiplying it by the distance. However, the direction of the force must be taken into account to determine the correct sign for the work.
 

1. What is work and tension problem?

Work and tension problem is a type of physics problem that involves calculating the amount of work done and tension in a system when an external force is applied.

2. How do you solve a work and tension problem?

To solve a work and tension problem, you need to first identify the external forces acting on the system and their direction. Then, use the equations for work and tension to calculate the values. Finally, check your answer to ensure it is reasonable and makes sense in the context of the problem.

3. What is the formula for calculating work in a work and tension problem?

The formula for calculating work is W = F * d * cosθ, where W is work, F is the external force applied, d is the displacement of the object, and θ is the angle between the direction of the force and the direction of the displacement.

4. How do you calculate tension in a work and tension problem?

To calculate tension, you need to use the equation T = mg + ma, where T is tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object.

5. What is the unit of measurement for work and tension?

The unit of measurement for work is joules (J) and the unit for tension is newtons (N). However, in some cases, tension may also be measured in pounds (lbs) or kilograms (kg).

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