Work integration
A 3.8 kg block is acted upon by a horizontal force F(x) = 24.0 -4.0x where the force is measured in Newtons if x is measured inmeters. The coefficient of kinetic friction between the block andthe flat surface is 0.19. The block is initially at x = 0 m. Whatdistance must the block travel if the net work done on the block byF(x) and friction combined is to be exactly zero? At what pointwhat point along the way does the net force on the block reachzero?

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(a) A block with a mass m is pulled along a horizontal surfacefor a distance x by a constant force F at an angle ? with respectto the horizontal. The coefficient of kinetic friction betweenblock and table is Âµk. Is the force exerted by friction equal toÂµkmg? If not, what is the force exerted by friction? (b) How muchwork is done by the friction force and by F ? (Donât forget thesigns.) (c) Identify all the forces that do no work on the block.(d) Let m = 2.00 kg, x = 4.00 m, Î¸= 37.0Â°, F = 15.0 N, and Âµk= 0.400, and find the answers to parts (a) and (b).

A mass m = 15 kg is pulled along a horizontal floor, with a coefficient of kinetic friction , for a distance d = 6.9 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of (thus on the incline it is parallel to the surface) and has a tension T = 33 N

1)What is the work done by tension before the block gets to the incline?

2)What is the work done by friction as the block slides on the flat horizontal surface?

3)What is the speed of the block right before it begins to travel up the incline?

4)How far up the incline does the block travel before coming to rest?

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1. A block is placed on a plane whose angle of inclination is 30˚. The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block
(A) remains stationary on the inclined plane.
(B) accelerates down the inclined plane.
(C) travels down the inclined plane at a constant velocity.
(D) travels up the inclined plane at a constant velocity.
(E) accelerates up the inclined plane.

2. An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30˚ with the horizontal and is 72 m long. The coefficient of friction between the plane and the object is 0.35. The speed of the object at the bottom of the plane is?

3. A 5-kg object slides down a frictionless surface inclined at an angle of 30˚ from the horizontal. The total distance moved by the object along the plane is 10 meters. The work done on the object by the normal force of the surface is?

4. A mass m = 2.5 kg is sliding along a frictionless table with initial speed v as shown in the figure. It strikes a coiled spring that has a force constant k = 500 N/m and
compresses it a distance x=5.0 cm. The initial speed v of the block was..?

5. The graph shows how the position of a particle depends on time. Which choice is closest to the instantaneous speed of the particle at t = 3s?
(A) 0.40 m/s
(B) 0.67 m/s
(C) 0.75 m/s
(D) 1.50 m/s
(E) 2.22 m/s

6. Calculate the work done by a force, F = 2x i, along the
path (0, 0) -> P₁(2, 0) -> P2(2, 2).

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