Friction and Work Homework: Find Distance d

[NAkid]

Homework Statement

In the figure, a block slides along a track from one level to a higher level, by moving through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is 6.1m/s; the height difference h is 0.82m; and the coefficient of kinetic friction is 0.60. Find d.

Homework Equations

K1+U(gravity,1) + W(friction) = K2 + U(gravity,2)

The Attempt at a Solution

Setting origin to the point where the block initially is, I have
.5m(v1)^2 + 0 (y1=0) - ukmgd (work due to friction) = 0 (v2=0) + mgy2

and solve for distance d

 

[||spoon||]

a simpler approach isto find the initial kinetic energy and then subtract from this the gravitational potential energy required to move higher. Then you will be able to find the velocity at the higher level.