Conservation of Energy of a block and spring

AI Thread Summary
The discussion focuses on a physics problem involving a 0.500 kg block on a frictionless surface, compressed against a spring with a spring constant of 625 N/m. The block is released, and the main tasks are to determine the maximum distance it travels up a frictionless incline at a 30° angle and its speed halfway to that height. The conservation of energy principle is applied, equating kinetic energy and potential energy. The user initially calculated the block's velocity at 11.18 m/s but needed guidance on how to proceed with the problem. Ultimately, they identified the relevant energy forms and successfully rearranged the equations to find the correct answers.
kimlu
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Homework Statement


A .500 kg block rests on a horizontal, frictionless surface as in the figure below. The block is pressed back against a spring having a constant of k=625 N/m, compressing the spring by 10cm to point A. Then the block is released.

a) Find the maximum distance d the block travels up the frictionless incline if θ= 30°

b) How fast is the block going when halfway to its maximum height?

Homework Equations



Kinitial+PEinitial= Kfinal+PEfinal

not exactly sure what other equations to use

The Attempt at a Solution



First I found the velocity of the block using KE=PEs (1/2mv^2=1/2kx^2) and ended up with equation of v=√kx/m and got 11.18 m/s for velocity but not sure what to do next or if I'm even doing this right I have the answers as shown in my attachment but I'm struggling to figure out how to get there please help I just started this topic in my AP Physics B course :(
 

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kimlu said:

Homework Statement


A .500 kg block rests on a horizontal, frictionless surface as in the figure below. The block is pressed back against a spring having a constant of k=625 N/m, compressing the spring by 10cm to point A. Then the block is released.

a) Find the maximum distance d the block travels up the frictionless incline if θ= 30°

b) How fast is the block going when halfway to its maximum height?


Homework Equations



Kinitial+PEinitial= Kfinal+PEfinal

not exactly sure what other equations to use

The Attempt at a Solution



First I found the velocity of the block using KE=PEs (1/2mv^2=1/2kx^2) and ended up with equation of v=√kx/m and got 11.18 m/s for velocity but not sure what to do next or if I'm even doing this right I have the answers as shown in my attachment but I'm struggling to figure out how to get there please help I just started this topic in my AP Physics B course :(
Hi kimlu, Welcome to Physics Forums.

This problem is largely about conservation of energy. You won't need to deal directly with velocities until the very end of part b.

Have you identified all the forms that energy can take in this problem? What are they?
 
The a) part suggests the maximum distance UP the incline plane, so what form of energy gets larger when height gets bigger with respect to the ground?
 
Hey guys I figured it out and identified the forms of energy as PEs initial=PEgfinal/ mgdsin30=1/2kx^2 and rearranged the formula for d and plugged in numbers, I believe I got the right answer now thanks for the help <:
 

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