Two Blocks on two inclines(Friction)

[ryan1180]

Homework Statement

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

Homework Equations

Ff=muFn
Vf^2=Vi^2+2ad

The Attempt at a Solution

I know that
Vf^2=Vi^2+2ad

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

since Vi=0
Vf^2=2ad
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.

 

[ryan1180]

Are my formulas correct at least?

 

[ehild]

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
Vf^2=2ad

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