# Two Blocks on two inclines(Friction)

#### ryan1180

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

A student has two ramps, both of which are at an angle of 30o. Ramp 1 is frictionless and ramp 2 has friction. The student also has two blocks, one for each ramp. She pushes the blocks up the ramps with the same initial velocity. The block on ramp 2 only travels a fraction f = 0.625 as far as the block on ramp 1 before coming to a stop (i.e. d2 = 0.625*d1) .

Find the coefficient of sliding friction between the block and ramp 2.

[PLAIN]https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys100/fall10/homework/07/IE_friction_fraction/frictionfraction.gif [Broken]

2. Relevant equations
Ff=muFn

3. The attempt at a solution

I know that

and my two formulas for acceleration are
a1 = -g*sin(30)
a2 = -g*sin(30) - μg*cos(30)

since Vi=0
since the Vf will be the same, the equations can be set equal to each other

2(-g)sin30(d)=2(-g)sin(30)-μgcos(30)(.625d)

I have tried this problem so many times and arrive at a final answer involving two variables. any help for finishing the problem would be greatly appreciated.

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#### ryan1180

Are my formulas correct at least?

#### ehild

Homework Helper
and my two formulas for acceleration are
a1 = -g*sin(30)
a2 = -g*sin(30) - μg*cos(30)
The accelerations are correct.

since Vi=0
The final velocities are zero. The initial velocities are equal.

the equations can be set equal to each other

2(-g)sin30(d)=2(-g)sin(30)-μgcos(30)(.625d)
You forgot the parentheses at the right-hand side around the acceleration. The correct equation is

2(-g)sin30(d)=2((-g)sin(30)-μgcos(30))(.625d)

ehild

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