Finding the Minimum Mass for Plunger-Spring Contact

In summary, the problem discusses a plunger resting on a spring with a given mass and distance. The question is how to determine the mass needed to keep the plunger in contact with the spring. Using the conservation of energy equation and the given equations, the solution involves analyzing the acceleration of the spring-mass and considering its limits.
  • #1
awiest82
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Homework Statement



A plunger of mass m rests on a spring with constant k. The spring is pressed down a distance x and released from rest. How large does the the mass need to be in order to keep the plunger in contact with the spring?

Homework Equations



PEf+KEf=PEi

kx-mg+N=0

The Attempt at a Solution



Using the Conservation of energy equation and solving for m, I get:

kx2/(2gh+vf2) = m

I have a suspicion that I somehow have to incorporate the second equation into the answer, but am stumped as to how I proceed.
 
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  • #2
Perhaps you can find a way through by analyzing the acceleration of the spring-mass and consider what limits this must be within.
 

1. What is a plunger on a compressed spring?

A plunger on a compressed spring is a simple machine that consists of a plunger attached to the top of a spring that is compressed or stretched. The plunger can be pushed down to compress the spring and released to allow the spring to expand.

2. How does a plunger on a compressed spring work?

When the plunger is pushed down, it compresses the spring, storing potential energy. When the plunger is released, the potential energy is converted into kinetic energy, causing the plunger to bounce back up. This repeated motion creates a spring-like effect that can be used for various purposes.

3. What are some real-life applications of a plunger on a compressed spring?

A plunger on a compressed spring is commonly used in shock absorbers, pogo sticks, and spring-loaded toys. It is also used in some mechanical clocks and watches to provide a ticking motion.

4. How does the spring affect the plunger's movement?

The spring's stiffness, also known as its spring constant, determines how much force is required to compress or stretch it. The stiffer the spring, the harder it is to compress or stretch, resulting in a more forceful rebound of the plunger.

5. Can the plunger on a compressed spring be adjusted?

Yes, the plunger on a compressed spring can be adjusted by changing the spring's stiffness or the length of the spring. This can be done by either changing the material of the spring or adjusting its shape or size. A larger or stiffer spring will result in a stronger rebound, while a smaller or less stiff spring will result in a weaker rebound.

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