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So I'm having some trouble with this problem can anyone help me out on how to solve it?

A 3.0 kg block is released from rest at the top of a 3.4 m high frictionless incline. At the bottom of the incline, the block encounters a spring with a constant of 4.0 x 102 N/m on a horizontal surface. The coefficient of friction between the block and the horizontal surface is 0.20. How far does the block slide while compressing the spring?

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I don't fully understand what to do or what equations to specifically use as the teacher didn't really give me anything about it.

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2 Answers 2

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Initially, you have some gravitational potential energy, namely $\mathrm{PE_{grav}}=mgh$. This is your initial potential energy.

Then at the end, you transform some of that energy into elastic potential energy, namely $\mathrm{PE_{spring}}=\dfrac12 kx^2$. This is your final potential energy.

Since there is friction, then it will do work on your system, namely $W_\mathrm{by \;friction}=-fd$.

Use conservation of energy:

$$\sum\mathrm{PE}+\mathrm{KE}+W_\mathrm{other \; forces}=\sum\mathrm{PE}'+\mathrm{KE}'$$

i.e. sum of initial potential energy + initial kinetic energy + work by other forces (specifically, non conservative forces, such as friction) = sum of final potential energies + final kinetic energy.

EDIT: assume that while the block is compressing the incline, friction is acting on it.

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  • $\begingroup$ How would you find the distance of the compression afterwards? $\endgroup$
    – Alp Tatar
    Jan 3, 2021 at 1:41
  • $\begingroup$ There is friction in the question its a coefficient of 0.2 $\endgroup$
    – Alp Tatar
    Jan 3, 2021 at 1:44
  • $\begingroup$ No friction on the incline, but friction when the block reaches the bottom, yes. The problem does not specify, but I would assume that the distance the block travels at the bottom is the same as the distance by which the spring is compressed. $\endgroup$
    – user256872
    Jan 3, 2021 at 1:46
  • $\begingroup$ Were you able to solve it? $\endgroup$
    – user256872
    Jan 3, 2021 at 1:51
  • $\begingroup$ Yeah I got 0.69m is that correct? $\endgroup$
    – Alp Tatar
    Jan 3, 2021 at 2:27
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First, using conservation of energy, calculate the kinetic energy of the block at the bottom of the incline before it encounters the spring. Then, calculate the work (using force times distance) done by the forces on the block, friction and the spring, to slow the block to zero kinetic energy, and that will give you the distance traveled.

I believe the problem wants you to assume the block is a rigid body in which case there is no "heating" of the block since there can be no internal dissipation of energy in a perfectly rigid body. In this case the force of friction only contributes to a change in the kinetic energy.

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  • $\begingroup$ Could you quickly run me through it? I'm still kind of confused. $\endgroup$
    – Alp Tatar
    Jan 3, 2021 at 1:32
  • $\begingroup$ We do not give specific answers to problems on this site; sorry. What is confusing you? $\endgroup$
    – John Darby
    Jan 3, 2021 at 1:33
  • $\begingroup$ "Then, calculate the work (using force times distance) done by the forces on the block, friction and the spring, to slow the block to zero kinetic energy, and that will give you the distance traveled." This doesn't make sense how would I find distance from it $\endgroup$
    – Alp Tatar
    Jan 3, 2021 at 1:43
  • $\begingroup$ Work is force times distance, and work equals change in kinetic energy. Suggest you consult a good physics text such as one by Halliday and Resnick. I see that @user256872 provided the specific relationships you need considering the potential energy of the spring. So I think you have what you need. $\endgroup$
    – John Darby
    Jan 3, 2021 at 3:47

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