# Find the maximum deflection of the spring

1. Feb 23, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
The 3.8-kg collar is released from rest at A and slides down the inclined fixed rod in the vertical plane. The coefficient of kinetic friction is 0.51. Calculate (a) the velocity v of the collar as it strikes the spring and (b) the maximum deflection x of the spring.

I have attached an image of the question.

2. Relevant equations

3. The attempt at a solution

I was able to find the velocity of the collar with:

U1 + K1 = U2 + K2 + F

K1 and U2 are 0

F is the friction force

0.5mv2 = mgh1 - F

Drawing a FBD of the collar shows that the Normal force (F = ukN):

N = mgsin(27)

0.5(3.8kg)v2 = (3.8kg)(9.81 m/s2)(0.57sin(63)) - (0.51)(0.57m)(3.8kg)(9.81m/s2)sin(27)

Solving for v gives me:

v = 2.7157

I can't seem to find the displacement of the spring though.

I realize that F = -kx and I need to find F to get x.

Looking at the practice question (identical scenario but different numbers) led me to believe that the answer should be:

F = mg - mgsin(27)

x = sqrt[mg-ukmgsin(27)/2700]

x = 103 mm
But it says this isn't correct and I'm not sure where I'm making my mistake.

Help is appreciated.

#### Attached Files:

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2. Feb 23, 2013

### TSny

Note that force and energy have different dimensions, so they can't be added together.