Maximum speed of a box compressing a spring on an inclined p

[harik2000]

Homework Statement

A box of mass m = 40kg is released from rest at thte top of a frictionless ramp. The ramp makes an angle theta = 45 degrees to the horizontal. After sliding fom the rigin a distance d = 2.00 m down the ramp, the box strikes a spring of force constant k = 500 N/m. The box compresses the spring momentarily stops, and then begins to slide back up the ramp. What is the maximum speed of the box?

Homework Equations

The Attempt at a Solution

mgsin(45) = kx
(9.81 * 40)sin45 = 500x
x= 0.5547

1/2(k)(x^2) = 1/2(m)(v^2)
v = 1.96m/s

Can anyone verify this pls?

 

[Mister T]

mgsin(45) = kx
(9.81 * 40)sin45 = 500x
x= 0.5547

1/2(k)(x^2) = 1/2(m)(v^2)
v = 1.96m/s

Can anyone verify this pls?

It doesn't look right to me. Any reason why you used force considerations to do the first part, and energy do do the latter part?

 

[harik2000]

It doesn't look right to me. Any reason why you used force considerations to do the first part, and energy do do the latter part?

I was trying to find the displacement provided when the ball compresses the spring the most however realized that I did not use potential energy mgh and I was confused. Can you show me the steps? I am confused.

 

[Mister T]

I was trying to find the displacement provided when the ball compresses the spring the most however realized that I did not use potential energy mgh and I was confused. Can you show me the steps? I am confused.

What part confuses you?

 

[harik2000]

I am confused about the potential energy so it would be equal to mgh = 1/2 k x^2 but how would that help solve for v?

 

[Mister T]

I am confused about the potential energy so it would be equal to mgh = 1/2 k x^2 but how would that help solve for v?

Solve it for x and tell us what you get.

 

[haruspex]

I am confused about the potential energy so it would be equal to mgh = 1/2 k x^2 but how would that help solve for v?

It won't.
First, please check you have stated the problem exactly.
Is it the whole problem or are there more parts? If there are more parts (and even if there aren't) consider the possibility that not all the information is relevant to finding the max speed.
Then consider at what point in the whole process you would expect max speed to be reached.