General Forces on Slope Problem

AI Thread Summary
The discussion revolves around deriving a general expression for mass m2 to ensure mass m1 moves at a constant speed up a ramp, incorporating friction (mu) and angle (theta). The equation simplifies to m2 = m1[sin(theta) + (mu)cos(theta)], allowing for exploration of conditions where m2/m1 is greater or less than 1. Participants express confusion about assigning numerical values to mu and theta without knowing the masses involved. Suggestions include experimenting with small and large angle values to find suitable mu and theta combinations. The conversation concludes with a clearer understanding of how to manipulate these variables to meet the specified conditions.
candycooke
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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.
 

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