# Final velocity of a mass moving through friction

1. Oct 20, 2016

### Jrlinton

1. The problem statement, all variables and given/known data
A block of 10 kg is pulled by a force of 100 N at and angle 30 degrees above the horizonal through a distance of 4 meters. Kinetic friction has a coefficient of 0.3.
How much work does friction do in that distance?
If its speed is 3 m/s at point a, what is its speed at point b?

2. Relevant equations

3. The attempt at a solution
For the first question I calculated the work of friction to be :
-u(Fn)(d)
(-0.3)((10kg*9.81m/s/s)-(100sin30))(4m)
-57.72 J

Now for the second part I took the kinetic energy of the mass moving at 3 m/s and added the work done by friction and set that equal to the final kinetic energy.
(0.5)(m)(v^2)+Wf=(0.5)(m)(v^2)
(0.5)(10kg)((3m/s)^2)-57.72J=(0.5)(10kg)(v^2)
-12.72 J= 5v^2
This is where i got stuck as the work done by friction was greater than the energy of the system to begin with. So according to this the object stopped before it even reached point b.

2. Oct 20, 2016

### Jrlinton

That is the work of friction as it is
(-u)(normal force)(d)
u=0.3
d=4.0m
Normal force= (m*g)-(FsinΘ)
with
m=10kg
g=9.81m/s/s
Magnitude of force= 100N
Angle of force above horizontal= 30 degrees

3. Oct 20, 2016

### Staff: Mentor

Um, where are positions a and b? Without a diagram or clear description it's hard to proceed.

Presumably the 100 N force makes some contribution to the horizontal motion, not just alleviating some of the friction force. So how much energy does it contribute to the scenario?

4. Oct 20, 2016

### Jrlinton

Sorry point a is x=o, point b x=4m
So:
FcosΘ*d+(0.5)(m)(v^2)+Work of friction=(0.5)(m)(vf^2)
100cos30*4+(0.5)(10kg)(3^2)-60=(0.5)(m)(v^2)
346.41+45-60=5v^2
v=8.14 m/s

5. Oct 20, 2016

### Staff: Mentor

Okay, the result looks good. Mind you, the lonely "kg" unit on the second line looks out of place without units being given for all the variables. So you may want to clean up the work before handing it in. Either include units for everything all the way though, use symbols for all values, or state that you're working with magnitudes and that units are ignored through the working (but definitely include the units on any final values!).