Work/Energy Problem: 50g Cube on 30 Degree Slope

[holtvg]

Homework Statement

A 50 g plastic cube slides up and down a 30 degree slope with friction. The plastic cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the plastic cube is released, what total distance will it travel up the slope before reversing direction if the coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope?

Homework Equations

spe=1/2kx^2 gpe=mgh ke=1/2mv^2 wf=uNd

The Attempt at a Solution

spe=wf+gpe

1/2*25*.1^2=-.20*9.8*cos(30 degrees)*d+.05*9.8*h

solve for d, can't solve equation, two unknowns? Tried to figure out h but couldn't.

 

[rock.freak667]

h is a vertical distance. So it makes a right angled triangle.

the hypotenuse is d and the height is h, and the angle is 30. I think you can find h in terms of d now.

 

[rl.bhat]

You can put h = d*sinθ.
In addition to the frictional force, one more force in acting on the plastic block. Which one?

 

[holtvg]

There's the x component of gravity and the normal force, but I'm not sure the x component of gravity does work. I know with respect to the cube the y component of gravity gives it potential energy. Does the spring do work tho, as it does apply a force f=-kx over a distance of 10 cm, that energy then becomes kinetic energy, then is transferred to friction and potential. Should i have kinetic energy in the equation? Or the moment just after the spring hits the cube.

ke=1/2mv^2

 

[rl.bhat]

When the cube is moving up, the frictional force and the x-component of the gravitational force act in the opposite direction. If d is the distance covered by the cube along the slope before coming to rest, then KE = (fg + fr )*d. You need consider PE separately.

 

[holtvg]

Ok you can't set h=dsin(theta) that gives you the wrong answer as i get about 140 cm. I did the math for the cube without friction and it moves about 50 cm, so if there was friction it would obviously be less than 50 cm.