# Box on ground, incline (with friction), ground: find Kinetic Energy

1. Jul 25, 2013

### questtosuccess

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

A 15 kg block slides along a horizontal frictionless surface 3.0 m above the ground at a constant speed of 2.0 m/s. The block then slides down an incline that makes an angle of 35° with the horizontal and has a coefficient of kinetic friction equal to 0.30. After reaching the end of the incline, the box continues sliding horizontally across the frictionless ground. Calculate the kinetic energy of the crate as it slides

a. along the upper surface.

b. along the ground.

2. Relevant equations

for a) KE= 1/2 mv2

for b) E1 = E2 + Wnon-conservative

3. The attempt at a solution

for a) KE=1/2 mv2 = 1/2 (15) (2)2 = 30 J

for b) I'm not quite sure where to consider the box sliding the ramp is at the moment... at the top (where y = 3 m) or the bottom (where y = 0 m)... regardless, this is how I did it.. but i'm pretty sure it's wrong

I began by finding the speed of the box when it's travelling down the ramp. I compared the energy of the box travelling along the upper surface, and the energy of the box going down the ramp (considering it to be at y = 0 m).

E1 = E2 + Wnon-conservative

1/2mv12 + mgy1 = 1/2mv22 + Ffdcos180

v2 = $\sqrt{}$ (2(mv12/2+ mgy1 - $\mu$k FNd (-1) )) /m

From here, I solved and found that v2 = 8.79 m/s
I had a problem already though.. I wasn't sure what "d" was supposed to be in this case ... for $\mu$k FNd cos180 ... I let d = 3m (is that right?)

Finally, I used the above info and compared the energy of the box going down the ramp (*** considering it to be at y = 3 m this time), and the energy of the box travelling along the lower horizontal surface.

E2 + Wnon-conservative = E3
mgy2 + 1/2mv22 + Ffdcos180 = 1/2mv32

Therefore,

KE3 = mgy2 + 1/2mv22 + Ffdcos180

I solved and got KE3 = 910 J

All of this seems very incorrect. I feel like I'm doing this all wrong. Please help !!! Thank you.

2. Jul 25, 2013

### Staff: Mentor

Hi questtosuccess, Welcome to Physics Forums.

You've got a good plan, using energy conservation methods to solve the problem. One thing though: you don't have to calculate velocity as an intermediate step if all you are looking for is the energy change.

Your initial value for the KE (for part (a)) is fine.

For the calculation of the energy change as the block slides down the ramp though, as you suspected you've got a bit of a problem with the friction force. What is the distance that the block moves in the direction of the friction force? (What surface does the friction force parallel?)

3. Jul 25, 2013

### haruspex

Also, I don't see where you calculate Ff or FN.

4. Jul 25, 2013

### questtosuccess

Thank you, I'm glad to be apart of this forum :)

I found the velocity of the box on the incline (v2) because I needed to plug it in to find the energy of the box at situation 3 (where it's travelling along the ground at 0 m).
How else would I be able to solve if I hadn't done that??

The distance isn't given.. that's what's confusing. The surface that the friction force parallels is the incline surface ... I still don't get it.

HARUSPEX: I calculated Ff .. it's μFn ... and Fn= mgcos35 .. I then solved and got that answer.

*It would be greatly appreciated if someone could let me know whether my final answer was correct. Thank you.

5. Jul 25, 2013

### Staff: Mentor

Kinetic energy is a quantity in its own right. Yes, it's related to velocity and mass by the formula (1/2)mv2, but you don't need to go from KE to velocity and back again if you have the relationship that relates all the changes in energies involved. You can work with the energy figures directly.
Well, with the given change in height and the known angle of the slope, how long is the slope?

6. Jul 25, 2013

### questtosuccess

Do you mean I should just set the equation as E1= E2 + Wnon-conservative = E3 ??

The slope is 35 degrees... and the change in height is 3m right? Because the top is 3m and the bottom is 0m ... ?

7. Jul 25, 2013

### Staff: Mentor

You start with some initial kinetic energy KEi that you calculated (30 J) before. As the box falls in elevation, gravitational PE will be converted to more KE for the box. You know how to calculate that amount. Also as the box slides on the surface of the ramp it will convert some KE to heat due to the action of friction, so the box loses some energy there. You know that amount of lost energy due to the work done by friction is given by ffd, where ff is the frictional force and d the distance along the surface that the force acts.

KEi + PEi = KEf + PEf + ffd

Solve for KEf. No velocities are needed for this part since you're actually looking for KEf and you calculated KEi previously.
Draw the picture. You should see a triangle... What side of the triangle does the box slide on? How long is that side?

8. Jul 26, 2013

### siddharth23

The final answer I got was 287.37 J. Is the answer given anywhere?

9. Jul 26, 2013

### questtosuccess

I just got it :D !!!! Thank you so much !! it's just trig ratios, so d= 3/sin35
Your help was much appreciated !!

10. Jul 26, 2013

### questtosuccess

Nope, no answer. But I got 282.1 J... so I'm assuming there was just an error in the rounding off throughout calculations.

Thanks for the reply ! :)

11. Jul 27, 2013

### siddharth23

Anytime mate :)

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