# Block, Ramp, Friction, and Spring work done

http://img412.imageshack.us/img412/7050/blockspringrampfrictionfy0.gif [Broken]

A man pulls a block of mass m = 20 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 33° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.2.

a) What is the work Wm done by the man?

b) What is the speed v of the block when it first reaches the horizontal surface?

c) What is the spring constant k of the spring?

d) How far up the incline d1 does the block rebound?

Relevant equations:
Wtotal = Change in Kinetic energy
Ffriction = Coefficient of friction(Fnormal)
Fspring = kx
(1/2)mv^2

I know there are the force of friction, the man, and gravity on the box. I started by saying:
Wman - Wgrav - Wfriction = Change in KE
Wgrav = m*g(in x-direction)*(Change in height) -->(20kg)(9.81m/s^2*sin33)(3.5sin33m)
Wfriction = (coefficient of friction)*m*g*distance -->(.2)(20kg)(9.81m/s^2)(3.5m)
Change in KE = 0
Wman = 823.919J, but this is not right...what am i doing wrong?

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What am i doing wrong with work done by the man? Isn't it just
Wman-Wgrav-Wfriction = 0
Wgrav = -m*g*h
Wfric = -(Coefficient of friction)(m*g)(distance)

PhanthomJay
Homework Helper
Gold Member
What am i doing wrong with work done by the man? Isn't it just
Wman-Wgrav-Wfriction = 0
Wgrav = -m*g*h
Wfric = -(Coefficient of friction)(m*g)(distance)
The work done by gravity is either -mgh or -mg(sin theta)*d. You used W_grav = -mg(sin theta)*d(sin theta) .

Also, when calculating the friction force, the normal force and the weight are not the same.

Wgrav = -(20kg)(9.81m/s^2)(sin33)(1.9m)

And if your turn your coordinate axis so the normal force is going in the positive y direction wouldn't that make the normal force equal and opposite of the weight of the block?

i figured it out

Wgrav = m*g*(sin theta)*d
Wfric = (Coefficient of friction)*(m*g*cos theta)*d

after that it was quite easy to figure out the rest.

Thanks PhanthomJay!