# Homework Help: Dynamics: Finding force exerted on a box traveling down a slope

1. Feb 25, 2012

### jaredogden

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

This is problem 13.70 from Beer and Johnston Vector Mechanics 9th ed.

A 300-g pellet is released from rest at A and slides with friction
along the surface shown. Determine the force exerted on the pellet
by the surface (a) just before the pellet reaches B, (b) immediately
after it has passed through B.

The drawing shows a pellet A on a declining slope, distance 1.2 m to B which is almost at the bottom of the slope. C is a flat surface. The radius of curvature between B and C is 0.8 m and the angle between them is 30°

2. Relevant equations

PE = mgz
KE = 1/2mv2
Fr = muk*N
Energy from Fr = FrΔx

3. The attempt at a solution

Since the pellet is at rest KEA = 0J, however PEA = (.3kg)(9.81m/s2)(1.2sin(30°))
(The angle between the horizontal and the 1.2m hypotenuse isn't given, but I just found it using opposite interior angles.)

so PEA = 1.7658 J

At B we will have KE and PE. Assuming C is at z = 0m we can use the radius of curvature and angle given to find zb

zB = 0.8 m - 0.8 m * cos(30°)
zB = 0.10718 m

so PEB = (.3kg)(9.81m/s2)(0.10718 m)
PEB = 0.31543 J

KEB = 1/2(.3 kg)vB2

Plugging all of this into the law of conservation of energy where EA = EB

1.7658 J = 0.31543 J + (1/2)(.3 kg)vB2
vB = 3.109 m/s

I got hung up here because I think that the work due to the frictional force should be subtracted from KEB + PEB in order to get the correct velocity the pellet would be traveling at. However, there is no coefficient of friction given in the problem.

I feel like I'm just missing something small here and my brain is just dead..

2. Feb 26, 2012

### LawrenceC

Would you sketch this?

3. Feb 26, 2012

### jaredogden

It is problem 13.70

#### Attached Files:

• ###### Vector Mechanics Dynamics.pdf
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4. Feb 27, 2012

### jhae2.718

From my reading of the problem, you're supposed to solve for the friction force on the block at the given points.

5. Feb 29, 2012

### jaredogden

Our teacher just posted an announcement that the problem should be a pellet sliding without friction.

The answer is 2.55N, I'm just unsure how to get here..