+244 A red sled with a mass of 10 kg is initially at rest near the top of a frictionless ramp that makes and angle 25° above the horizontal. The sled is initially 5.0 m from the bottom of the incline, shown in the figure below. When the sled is released it slides down the ramp and encouters a rough horizontal surface with a coefficient of kinetic friction of 0.21 and slides to a halt in some distance, d. What is this distance, d?
20 m
10 m
15 m
5.0 m
25 m
1. Use trig to find height of ramp
2. Find the gravitational potential energy when the sled is at top of ramp
All of the potential energy will be converted to kinetic energy when it reaches the bottom of ramp.
3. Set potential energy equal to kinetic energy and solve for velocity
You now know how fast the sled is going when it reaches the rough horizontal surface
shortcut: acceleration on rough surface = g * coeficient of friction (you should figure out why if you are not familiar)
4. Divide initial speed bby acceleration on rough surface to find time on rough surface before the sled stops
5. Plug time, acceleration and initial velocity into kinetic formula and solve for d: d = vt + (a/2)t^2
