A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle alfa (see figure). Initially the truck is moving downhill at speed v0. After sliding downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle beta. The truck ramp has a soft sand surface for which the coefficient of rolling friction is f. After an unknown distance D along the ramp the truck comes to a halt. The acceleration of gravity is g. What is the total work Wf done by the friction force on the runway ramp?

A frictionless plane is 10.0 m long and inclined at 37.0°. A sled starts at the bottom with an initial speed of 6.00 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi. Both sleds reach the bottom of the incline at the same moment. (a) Determine the distance that the first sled traveled up the incline. m(b) Determine the initial speed of the second sled. m/s

Consider the incline shown in the figure with inclination angle θ and height h. The coefficient of kinetic friction between a block of mass m and the incline changes along its surface. From A to B it has a value of μ1, and from B to C its value is μ2. The block (not shown) is given an initial velocity up the incline at point A with a magnitude vA.   A) What is the value of vA for which the block will reach the top of the incline (point C) with zero kinetic energy? Your answer should be written in terms of the quantities given in the statement.   B) Show that for the block to surpass point B, the initial speed at A should satisfy the inequality  vA > √[ (2/3)gh(1+μ1cotθ) ]

An extreme skier, starting from rest, coasts down a mountain that makes an angle of 35.3 ° with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.115. She coasts for a distance of 18.5 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 4.32 m below the edge. How fast is she going just before she lands?

A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.63 m above the bottom of the chute with an initial speed of 1.41 m/s . The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.273 . How far from the bottom of the chute does the toy zebra come to rest? Assume ?=9.81 m/s2 .

A truck is traveling at 14.7 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 19 ° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.789. How far, in meters, does the truck skid before coming to a stop?

A truck is traveling at 10.0 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 11 ° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.933. How far, in meters,  does the truck skid before coming to a stop?

Two crates of fruit  are released from the top of a ramp inclined at 30 degrees from the horizontal and 4.5 meter long. The two crates consist of  an apple crate of mass 20 kg that is placed in front of a watermelon crate of mass 80 kg.  The apple crate has a coefficient of friction of 0.20 while the watermelon crate has a coefficient of friction of 0.15. How long does it take the apple crate to reach the bottom of the incline if it needs to travel a distance of 4.5 meters?

A 52.5-kg sled is pulled across a horizontal icy surface as in the figure. The horizontal pulling force of magnitude P is directed opposite to a constant  35.0-N kinetic friction force. Starting from rest, the sled acquires a final speed of  2.25 m/s after being pulled a distance of  20.0 m. Two forces act on a sled that is on a horizontal surface. An arrow labeled vector fk extends from the left side of the sled and points left. An arrow labeled vector P extends from the right side of the sled and points right. The lengths of the arrows are approximately equal to each other. What is the magnitude P of the pulling force? N?

On a windy day, you decide to use a small homemade parachute to travel up a 7.4 degree hill on your frictionless rollerblades. You begin from rest at the bottom of the hill and travel a distance of 23 meters up the hill (measured along the incline), reaching a speed of 14 m/s. You have a mass of 60 kg. Determine the force the wind exerts on the parachute, assuming the force the wind exerts is parallel to the surface of the incline. Use conservation of energy.