Principle of Work and Energy: Spring and Mass

In summary, the problem involves a 65-kg cylinder being released from rest and falling 300 mm, causing the spring to stretch 0.6 m and experience a tension of 75. By using the displacement equation and setting the tension force equal to the potential energy of the spring, the speed of the cylinder after falling 300 mm can be determined. The free body diagram also shows potential gravitational energy and a tension force acting in the opposite direction. More details are needed to fully solve the problem.
  • #1
Peter P.
23
0

Homework Statement


When the 65-kg cylinder is released from rest, the spring is subjected to a tension of 75. Determine the speed of the cylinder after it has fallen 300. How far has it fallen when it momentarily stops?

Given Diagram:
Prob.14-93.jpg



Homework Equations





The Attempt at a Solution


I started with a displacement equation. When the mass has fallen 300 mm (or 0.3 m), the string should stretch 0.6 m. I think that i can use F = kx, where F = T. So then the spring is already stretched by 0.25 m. From the free body diagram of the cylinder, i know that there will be potential gravitational energy, and a tension force acting in the opposite direction. Heres my long shot, but can i make the tension be represented by the potential energy of the spring (Vs = 0.5ks2). Then i get a little lost in whether or not i can do that.

Thanks in advance for any help.
 
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  • #2
Hi PeterP,

you are on the right track, go ahead. ehild
 

1. What is the principle of work and energy?

The principle of work and energy states that the work done on an object is equal to the change in its kinetic energy. It also states that energy cannot be created or destroyed, only transferred from one form to another.

2. How is the principle of work and energy applied to a spring and mass system?

In a spring and mass system, the potential energy stored in the spring is converted into kinetic energy as the spring is compressed or stretched. This kinetic energy is then transferred to the mass, causing it to move. When the spring returns to its original position, the kinetic energy is converted back into potential energy.

3. What is the relationship between the force applied to a spring and the displacement of the mass?

According to Hooke's Law, the force applied to a spring is directly proportional to the displacement of the mass from its equilibrium position. This means that the greater the force applied, the more the spring will stretch or compress, resulting in a larger displacement of the mass.

4. Can the principle of work and energy be applied to non-conservative forces?

No, the principle of work and energy can only be applied to conservative forces, which are forces that do not dissipate energy and can be fully recovered. Non-conservative forces, such as friction, do not follow this principle because they dissipate energy as heat or sound.

5. How is the principle of work and energy related to the conservation of mechanical energy?

The principle of work and energy is a direct result of the law of conservation of mechanical energy, which states that the total amount of mechanical energy in a system remains constant as long as there are no external forces acting on it. This means that the work done on an object will result in a change in its kinetic or potential energy, but the total amount of energy will remain the same.

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