Work/Potential Energy of a Spring

In summary, the conversation discusses various problems involving work and potential energy. The first two problems involve finding the work and change in potential energy of a 2kg mass raised 2m vertically, with the answers being 39.2J for both. The next two problems involve a spring with a spring constant of 50N/m being compressed by 0.1m, with the work and change in potential energy being 0.25J for both. The final problem involves finding the final speed of a 0.05kg mass held against a spring with a spring constant of 50N/m and compressed by 0.1m, with the final answer being the square root of 10 meters per second. However,
  • #1
JJBrian
20
0

Homework Statement



a)how much work is done by gravity as a 2kg mass is raised 2m vertically?

b)what is the change in gravitation potential energy of a 2kg mass raised 2m vertically?

c)How much work is done by a spring with a spring constant k = 50N/m as it is compressed by 0.1m from its relaxed position?

d) what is the change in the potential energy of a spring with spring constant k = 50N/m as it is compressed by0.1m from is relaxed position?

e) A 0.05kg mass is held against a spring( with spring constant k = 50N/m) while the spring is compressed by 0.1m. The mass is released and accelerated by the spring. What is the final speed of the mass?

The Attempt at a Solution



A. Wg= mgh wg = (2)(9.8)(2) = 39.2J
B. PE = mgh PE = (2)(9.8)(2) = 39.2J
C. Ws = 1/2kx^2 Ws = 1/2(50)(.1)^2 = 0.25J
D. Us = 1/2 kx^2 Us = 1/2(50)(.1)^2 = 0.25J
E. I don't know...
W = change KE
attempt 1/2kx^2 = 1/2mv^2
1/2(50)(.1)^2 = 1/2(.005)v^2
vf = sqrt(10)m/s


can someone check my work?
I need some help and explanation for problem e.
Im not too sure about the signs.
 
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  • #2
You seem to be missing a few negative signs...It might help you to find them by looking at the definition of work done by any force [itex]\textbf{F}[/itex] in moving an object form point [itex]\textbf{a}[/itex] to point [itex]\textbf{b}[/itex]...what is that definition (it involves an integral and a dot product)?
 

1. What is the definition of work and potential energy of a spring?

The work of a spring is defined as the force exerted on an object by the spring as it changes its position. This is typically represented by the formula W = Fd, where W is work, F is force, and d is the distance the object moved. Potential energy of a spring is the energy stored in a spring when it is compressed or stretched, and it is given by the formula PE = 1/2kx^2, where k is the spring constant and x is the displacement from its equilibrium position.

2. How is the work and potential energy of a spring related?

The work done by a spring is directly related to its potential energy. This means that as the spring is compressed or stretched, the potential energy increases, and when the spring returns to its equilibrium position, the potential energy returns to zero. The work done on the spring is equal to the change in potential energy, which is given by the formula W = ΔPE = PEf - PEi.

3. What factors affect the work and potential energy of a spring?

The work and potential energy of a spring are affected by several factors, including the spring constant, the displacement of the spring, and the mass of the object attached to the spring. The greater the spring constant, the larger the amount of work and potential energy. Similarly, the greater the displacement and mass, the more work and potential energy will be produced.

4. Can the work and potential energy of a spring be negative?

Yes, the work and potential energy of a spring can be negative. This can happen when the spring is stretched and the object attached to it moves in the opposite direction of the applied force. In this case, the work done by the spring is negative, and the potential energy of the spring will also be negative.

5. What are some real-life applications of work and potential energy of a spring?

The work and potential energy of a spring have many real-life applications, such as in shock absorbers, trampolines, and pogo sticks. They are also used in various mechanical devices, such as car suspensions, to store and release energy. Additionally, the principles of work and potential energy of a spring are essential in understanding and designing springs for different purposes.

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