# Mechanical Energy Question Involving a Spring

#### Dante Tufano

1. In the figure below, a block of mass m = 3.20 kg slides from rest a distance d down a frictionless incline at angle θ = 30.0° where it runs into a spring of spring constant 445 N/m. When the block momentarily stops, it has compressed the spring by 21.0 cm.

Here is the image: http://www.webassign.net/hrw/hrw7_8-41.gif

(a) What is the distance d?

(b) What is the distance between the point of first contact and the point where the block's speed is greatest?

2. Okay, so using the variable s as the amount the spring is compressed, I determined that mg(d+s)sin(theta)= (1/2)ks^2

3. Okay, so using the above equation, I solved for d and got the answer to part A. It's part B that I'm lost on. Apparently, the distance is not zero like I initially thought, so I'm not quite sure what to do. It says to write K as a function of descent distance after the spring contact is made, but I have no idea what that function would be, nor how to set it up.

#### Dante Tufano

Anybody? I can't move on with the homework until I figure this one out.

#### tiny-tim

Homework Helper
Hi Dante! (have a theta: θ and try using the X2 tag just above the Reply box )
mg(d+s)sin(theta)= (1/2)ks^2

Apparently, the distance is not zero like I initially thought, so I'm not quite sure what to do. It says to write K as a function of descent distance after the spring contact is made, but I have no idea what that function would be, nor how to set it up.
Your equation is fine. Now adapt it to find the KE (is that your K?), then differentiate it to find where the KE is a maximum …

what do you get? #### Dante Tufano

Oh wow, I plugged everything in and it worked out, I probably should have been able to see the answer. Thanks a lot!

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