Problem with when to use Force and Energy. What compresses spring/

  • #1
physicsissohard
19
1
Homework Statement
A mass of 20 kg is released from rest from the top of a fixed inclined plane of inclination 53 deg and height 4 m. At the bottom of the inclined plane, there is a massless spring of length 2 m. Find the maximum compression of the spring.(k=10000 N/m) take g=10m/s2
Relevant Equations
ME1=ME2
This is how I tried to do it, which is the most direct. The force that the mass exerts on the spring is mgsin(53). and I equated that to kx. and found x. but apparently, this is wrong and the teacher told me a different method.
(ME)1=(ME)2 due to conservation of mechanical energy
20∗10∗4=20∗10(2−x)∗0.8+0+0.5∗10000∗x^2 on LHS there is no kinetic energy and the potential energy of the block is the only thing on the left. And RHS there is no kinetic energy but the potential energy of the block and spring is there. And from here you just need to solve the quadratic. I understand this method and see nothing wrong with but I don't understand what is wrong with mine. I think I even get where the difference is coming actually. It's even more intuitive that in the second method, you observe that when the block collides with the spring it compresses very much and comes back to less than the original length, which doesn't take it into account. But I don't understand why it compresses more cuz the same force is applied, so it moves the same distance. Just can somebody elucidate why force doesn't only determine the compression? It's hookes Law I don't see what's wrong though.
 
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  • #2
physicsissohard said:
Homework Statement: A mass of 20 kg is released from rest from the top of a fixed inclined plane of inclination 53 deg and height 4 m. At the bottom of the inclined plane, there is a massless spring of length 2 m. Find the maximum compression of the spring.(k=10000 N/m) take g=10m/s2
Relevant Equations: ME1=ME2

20∗10∗4=20∗10(2−x)∗0.8+0+0.5∗10000∗x220∗10∗4=20∗10(2−x)∗0.8+0+0.5∗10000∗x^2 on LHS there is no kinetic energy and the potential energy of the block is the only thing on the left.
Can you rewrite this equation using symbols first and then substitute numbers? I have a hard time deciphering expressions like 0.5∗10000∗x220∗10∗4. Also, I can see a LHS (left hand side) and a RHS (right hand side) but I also see a MHS (middle hand side). What's that about?

Please use the LaTeX editor for your equations.
 
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Likes Lnewqban
  • #3
sry it was a typo. there is no MHS
 
  • #4
physicsissohard said:
But I don't understand why it compresses more cuz the same force is applied, so it moves the same distance. Just can somebody elucidate why force doesn't only determine the compression? It's hookes Law I don't see what's wrong though.
Consider how the force with which the spring reacts changes during the distance x.
Is that force greater or lesser than kx at the beginning of the compression stroke?
 

FAQ: Problem with when to use Force and Energy. What compresses spring/

What is the difference between force and energy?

Force is a vector quantity that causes an object to undergo a change in motion, measured in newtons (N). Energy is a scalar quantity that represents the capacity to do work, measured in joules (J). While force can cause an object to move or change shape, energy quantifies the work done by the force.

How does force compress a spring?

Force compresses a spring by applying pressure to it, causing it to deform. According to Hooke's Law, the force required to compress or extend a spring is directly proportional to the distance it is stretched or compressed, expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.

When should I use the concept of force instead of energy?

Use the concept of force when you need to describe the interaction between objects that causes a change in motion or shape. For example, when calculating the acceleration of an object due to a push or pull. Use energy when you need to quantify the work done or the potential to do work, such as in calculating kinetic or potential energy.

How is energy stored in a compressed spring?

Energy is stored in a compressed spring as elastic potential energy. When a force compresses the spring, work is done on the spring, and this work is stored as potential energy. The amount of stored energy can be calculated using the formula U = 1/2 k x^2, where U is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

What role does the spring constant (k) play in compressing a spring?

The spring constant (k) is a measure of the stiffness of a spring. It determines how much force is required to compress or extend the spring by a certain distance. A higher spring constant means the spring is stiffer and requires more force to compress or extend it by the same amount compared to a spring with a lower spring constant.

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