# Conservation of Energy, Down an Incline with a Spring

Tags:
1. Feb 21, 2017

### RavenBlackwolf

1. The problem statement, all variables and given/known data
A 4.0 kg block starts at rest and slides a distance d down a frictionless 35.0 incline, where it runs into a spring. The block slides an additional 16.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 429 N[PLAIN]https://homework2.math.pitt.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3D.pngm [Broken] .

a) What is the value of d?
b) What is the distance between the point of first contact and the point where the block's speed is greatest?
2. Relevant equations
Ui+Ki=Uf+Kf
US=1/2kx2
UG=mgh
K=1/2mv2
3. The attempt at a solution
a) This one I got
1/2kx^2=mgΔh
1/2(429)(.162)=mgΔh
Δh=.244
b) This one I'm not sure of
1/2mv2+mgh=1/2mvf2+mg((.16-x)sin(35))+1/2kx2
I got that the velocity at contact is .972 m/s but how do I get the final velocity value? I need it to use the conservation of energy law the way I set it up. I've found similar questions to this online but none of them provide actual explanations/calculations for this part. I'm aware that it accelerates still once it hits the spring but then what?

#### Attached Files:

• ###### Capture.PNG
File size:
4.3 KB
Views:
16
Last edited by a moderator: May 8, 2017
2. Feb 21, 2017

### Staff: Mentor

That's the key. As long as it's accelerating (downward), it's speed continues to increase. So what condition must exist at the point of maximum speed?

3. Feb 21, 2017

### RavenBlackwolf

The acceleration in the x direction would be 0 correct? I thought of that before but I got lost because wouldn't I need time if I'm using the kinematics equations? Are they what I should use to find vf or should I be using an energy concept?

4. Feb 21, 2017

### Staff: Mentor

Right. Now figure out where (not when) the acceleration would be zero. Then use energy methods to find the speed.

5. Feb 21, 2017

### RavenBlackwolf

Where as in Δx? Don't I need the vf to find that though? That's the only reason I wanted to find vf at all. All I have is the .16m when the spring is compressed to the fullest and v=0 I believe ax is zero there too but that can't be the answer. I feel like I'm missing something but I can't figure out what because I've been working this problem too long. Its x acceleration is positive (at least the way I'm modeling it) when it hits the spring then it gets smaller, hits zero, then goes negative. I don't understand where I'm gathering distances from this though. The value I need is the distance at which the acceleration is zero and the velocity is maximized. Would it be halfway down then?

6. Feb 21, 2017

### Staff: Mentor

You have no need to actually find the max speed, just the position where it is attained.

If the acceleration were zero at that point, it would just sit there. But it doesn't.

Don't guess. Hint: Use dynamics. Analyze the forces as the spring is compressed.

7. Feb 21, 2017

### Staff: Mentor

You can skip this step, since you're not asked to find the max speed.