# Homework Help: A block of mass m=0.2 kg, is pushed by a spring of stiffness k=300 N/m

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1. Apr 24, 2017

### selhai97

I am currently taking a physics class and I'm studying for the final and I've been stuck on this problem and haven't been able to find help from the book nor help from online.

The professor said the answer was .56m, but I've been trying formulas for about an hour now and haven't been getting anything close to that.

1. The problem statement, all variables and given/known data

A block of mass m=0.2 kg, is pushed by a spring of stiffness k=300 N/m, initially compressed by A=10cm, up the 30° wedge. If the friction coefficient between the block and the wedge is 0.6, how far will the block pass in m along the wedge before it stops?

2. Relevant equations

I think:
ω = √(k/m)
T = (2π)/ω
x = Acos(ωt + φ)

3. The attempt at a solution

ω = √(300/.2) = 7.7
T = (2π)/7.7 = .82
x = (10)cos(7.7*.82) = 9.99

Like I said, I've been trying different formulas for about an hour now, so I don't think I'm using the right ones.

Any help would be amazing, thank you!

2. Apr 24, 2017

### PeroK

The problem involves a wedge at an angle, gravity, a spring and friction? I'm not sure it's a good idea to use SHM, which would be about the frequency of oscillations of the system.

3. Apr 24, 2017

### PeroK

PS You might want to check those numbers. Do you have a diagram?

4. Apr 24, 2017

### selhai97

No, no diagram, that's all the information that I was given.

5. Apr 24, 2017

### PeroK

The difficulty as I see it is that on a $30°$ angle, a coefficient of friction of $0.6$ more than cancels gravity. In any case, the nett force is low. With those numbers, it's effectively just the spring, with a small variation due to the slope.

Without the slope, it should move $20cm$.

Also, even if you take friction out of the equation, the PE of the mass is low compared to the spring. Even a mass hanging on that spring wouldn't stretch it much. You could work that out.

I'd leave it. It doesn't look right to me.

6. Apr 24, 2017

### selhai97

Alright, well thanks anyways! I really appreciate it.

7. Apr 24, 2017

### Staff: Mentor

The problem doesn't specify if the block is attached to the spring or whether it is unattached, or what is to be considered the block's starting position (before the spring compression or after?).

Either way I'd suggest an energy approach.

8. Apr 24, 2017

### PeroK

Yes, of course, if the mass was pushed down on the spring and not attached to it!

9. Apr 24, 2017

### selhai97

You wouldn't use something like this right?
max = -mgsinθ
vxf2 = vxi2 + 2aΔx

10. Apr 24, 2017

### Staff: Mentor

Nope. I'd deal directly with the energies (kinetic and potential). The only tricky bit is handling the spring action since the block and spring become disengaged at some point.

11. Apr 24, 2017

### selhai97

So PE = mgh and KE = (½)mv2?

Are there other equations that involve the A and k and μ?

I'm sorry if I'm so lost, physics is my hardest subject.

12. Apr 24, 2017

### Staff: Mentor

Look into formulas pertaining to the potential energy stored by a spring and the energy lost to friction.