7. Friction, Inclines, Systems

Inclined Planes with Friction

Multiple Choice
A 3-kg block is at rest on an adjustable ramp. When the ramp is tilted to a 20° angle, the block slides with constant velocity. What is the coefficient of kinetic friction between the ramp and the block?
Open Question
A bicycle coasting at 8.0 m/s comes to a 5.0-m-long, 1.0-m-high ramp. What is the bicycle's speed as it leaves the top of the ramp?
Open Question
A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 6.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 3.40 m from the top of the incline?
Open Question
A very slippery block of ice slides down a smooth ramp tilted at angle θ. The ice is released from rest at vertical height h above the bottom of the ramp. Find an expression for the speed of the ice at the bottom.
Open Question
A snowboarder glides down a 50-m-long, 15 degree hill. She then glides horizontally for 10 m before reaching a 25 degree upward slope. Assume the snow is frictionless. (b) How far can she travel up the 25 degree slope?
Open Question
FIGURE P2.64 shows a fixed vertical disk of radius R. A thin, frictionless rod is attached to the bottom point of the disk and to a point on the edge, making angle Φ (Greek phi) with the vertical. Find an expression for the time it takes a bead to slide from the top end of the rod to the bottom.
Open Question
A skier is gliding along at 3.0 m/s on horizontal, frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 15 m/s. (a) What is the length of the incline?
Open Question
A car traveling at 30 m/s runs out of gas while traveling up a 10 degree slope. How far up the hill will it coast before starting to roll back down?
Open Question
A 25.0-kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35. (b) At this angle, find the acceleration once the box has begun to move.
Open Question
An 8.00-kg block of ice, released from rest at the top of a 1.50-m-long frictionless ramp, slides downhill, reaching a speed of 2.50 m/s at the bottom. (b) What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of 10.0 N parallel to the surface of the ramp?
Open Question
A 5.0 kg wooden sled is launched up a 25° snow-covered slope with an initial speed of 10 m/s.a. What vertical height does the sled reach above its starting point?
Open Question
A rubber-wheeled 50 kg cart rolls down a 15 degrees concrete incline. What is the magnitude of the cart's acceleration if rolling friction is (a) neglected and (b) included?
Open Question
A motorcycle daredevil plans to ride up a 2.0-m-high, 20° ramp, sail across a 10-m-wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts up the ramp. He is going 11 m/s at that instant, and the rolling friction of his rubber tires (coefficient 0.02) is not negligible. Does he survive, or does he become crocodile food? Justify your answer by calculating the distance he travels through the air after leaving the end of the ramp.
Open Question
(II) Show that if a skier moves at constant speed straight down a slope of angle θ (Example 5–6), then the coefficient of kinetic friction between skis and snow is μₖ = tanθ. Ignore air resistance.
Open Question
A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m?

(b) Assume an effective coefficient of rolling friction equal to 0.10.