General Forces on Slope Problem

[candycooke]

a) Find a general expression for mass m2 so that m1 will move at a constant speed up the ramp. Your answer will be based on (mu) and (theta).
b) Give a numerical value for (mu) and (theta) so that m2/m1 > 1
c) Give a numerical value for (mu) and (theta) so that m2/m1 < 1


Fg2 = m2g
Fg1x = m1gsin(theta)
Ff = (mu)Fn
Fn = Fg2y
a = 0m/s2
Fnet = ma
g = 9.8 m/s2

Fnet = Fg2 - Fg1x - Ff
0 = m2g - m1gsin(theta) - (mu)cos(theta)
m2g = m1gsin(theta) + (mu)cos(theta)
m2 = [m1gsin(theta) + (mu)cos(theta)] / g

My problem is that I don't understand how to give a numerical value for (mu) and (theta) so that m2/m1 > or < 1 without also determining the mass of either m1 or m2 since they are both a part of the general equation. Is it even possible without also giving a numerical value to one of the masses?? Any clarification is greatly appreciated.

 

[Doc Al]

0 = m2g - m1gsin(theta) - (mu)cos(theta)

That last term--the friction force--is missing a few factors. Redo it and the solution may be clearer.

 

[candycooke]

0 = m2g - m1gsin(theta) - (mu)m1gcos(theta)
m2g = m1gsin(theta) + (mu)m1gcos(theta)
m2 = [m1gsin(theta) + (mu)m1gcos(theta)] / g

Although the equation makes a bit more sense, I'm still confused about how to give a numerical value for (mu) and (theta) so that m2/m1 > or < 1 without also determining the mass of either m1 or m2 since they are both a part of the equation.

 

[Doc Al]

0 = m2g - m1gsin(theta) - (mu)m1gcos(theta)
m2g = m1gsin(theta) + (mu)m1gcos(theta)
m2 = [m1gsin(theta) + (mu)m1gcos(theta)] / g

Good. Now further simplify that last expression: Start by factoring out the m1 and the g.

 

[candycooke]

m2 = [m1gsin(theta) + (mu)m1gcos(theta)] / g
m2 = [m1g[sin(theta) + (mu)cos(theta)]]/g
m2 = m1[sin(theta) + (mu)cos(theta)]

So factoring has eliminated g but m1 and m2 are sill part of the equation, leaving me just as confused as before.

 

[Doc Al]

You're almost there. Write it as m2/m1 = ?

Now you get to play around with theta and mu. Hint: Compare a small angle (~ 5 degrees) with a bigger angle (~ 85 degrees).

Remember: All you need to do is make up a few values that satisfy the requirements.

 

[candycooke]

Thank you for your help Doc Al. It all makes sense now.