energy lost in friction:
mg*cosTheta*mu*distanceupplane
KE lost going up the plane:
mg*SinTheta*distanceupplane
add those, set them equal to initial KE.
A 2.0 lb block is given an initial speed of 4.0 ft/sec up an inclined plane starting from a point 2.0 feet from the bottom as measured along the plane. If the plane makes an angle (theta = 30 degrees) with the horizontal and the coefficient of friction is 0.20, how far up the plane will the block travel?
...What I've done so far:
Since the total energy is conserved, I set E(initial) = E(final), which is also
Work (if any is done) + PE(initial) + KE(initial) = PE(final) + KE(final) + (Energy "lost" due to friction)
I'm ignoring the 2.0 starting point for the sake of the question, which makes PE(initial) 0, and since there's no work, the equation ends up being:
KE(initial) = PE(final) + (Energy "lost" due to friction) (...Final kinetic energy will also be equal to 0.)
Am I supposed to be subtracting friction force here? The way I've drawn my diagram, the friction force is pointing in the negative x direction, with the block moving up the incline in the positive x direction. My answer for d is 0.760 ft, which doesn't seem to work when I plug it back into the equation.
Any assistance?
3 answers
OH! I forgot to take the x component of Fg into account! Thanks!
...I'm still confused. It's still not turning out right.