- 20

- 0

**1. Homework Statement**

A block is sitting on a ramp with a spring behind it, which we are supposed to imagine we are holding. The mass of the block is 20 kg, the angle of the ramp is 30 degrees, and the spring constant is 500 N/m.

1) You pull so the block is accelerating at 4 m/s^2 up the ramp. How far does the spring stretch?

2) Now you are on a ramp with the following coefficients of friction: static friction coefficient=0.3 and the kinetic coefficient=0.2. You are initially holding the free end of the spring. You pull the spring so the block is accelerating at 4 m/s up the ramp, how far is the spring stretched?

**2. Homework Equations**

F=ma

F=kx

**3. The Attempt at a Solution**

1)Can someone tell me if the way I solved for the stretch of the spring is correct? I'm not sure how to do it or how to incorporate acceleration into the equations in any other way.

ΣFx=mgsinΘ=ma

Fspring=mgsinΘ=kx

mgsinΘ=kx

ma=kx

(20kg)(4m/s^2)=500 N/m)x

x=0.16m

2) ΣFx=mgsinΘ-f

_{k}=ma

ΣFy=n-mgcosΘ

n=mgcosΘ

-I assume we use kinetic friction because the block is moving.

f

_{k}=μ*n=0.2mgcos(30)=33.95N

I'm not sure where to go from there to get x unless I set ΣFx=mgsinΘ-fk=kx but that doesn't seem right. But I did find in previous problems that Fspring=mgsinΘ=kx, so should I use ΣFx=kx-fk=ma ??? Or is this entirely wrong?