Problem 5. A block of mass m = 5.00 kg is released from rest from point A and slides on the frictionless track shown on Fig. 5.Determine: (a) the block's speed at ponts B and C. (b) The work done by the gravitational force on the block as it moves from A to C. Problem 6. A ball of mass m = 1.80 kg is released from rest at a height h = 65.0 cm above a light vertical spring of constant k, as in Fig. 6. The ball strikes the top of the spring and compresses it a distance d= 9.00 cm(see Fig. 6). Neglecting any energy losses during the collision, find: (a) the speed of the ball just as it touches the spring. (b) the force constant k of the spring.

Suppose a car travels 108 km at a speed of 25.0 m/s, and uses 2.20 gallons of gasoline. Only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (The energy content of gasoline is 1.3 ✕ 108 J per gallon.)(a) What is the force exerted to keep the car moving at constant speed? N (b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s? gallons

A conservative force F is in +x-direction and has a magnitude F(x)=3.00/(x+0.080)4 N. Let U(x) approach 0 when x approaches infinity. An object with mass 5.00 kg is released from rest at x = 0 and moves in the +x-direction. If F is the only force action on the object, what is the object's speed when it reaches x = 0.500 m?

A student, starting from rest, slides down a water slide. On the way down, a kinetic frictional force (a nonconservative force) acts on her. The student has a mass of 81 kg, and the height of the water slide is 11.8 m. If the kinetic frictional force does -5.1 × 103 J of work, how fast is the student going at the bottom of the slide?

A single conservative force acts on a 4.70-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 0.96 m to x = 7.50 m, calculate the following. (a) the work done by this force on the particle 81.488 J (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 7.50 m if its speed is 3.00 m/s at x = 0.96 m J

A 199 kg crate hangs from the end of a rope of length L = 13.7 m. You push horizontally on the crate with a varying force F to move it distance d = 4.25 m to the side (see the figure). (a) What is the magnitude of F when the crate is in this final position? During the crate's displacement, what are (b) the total work done on it, (c) the work done by the gravitational force on the crate, and (d) the work done by the pull on the crate from the rope? (e) Knowing that the crate is motionless before and after its displacement, use the answers to (b), (c), and (d) to find the work your force F does on the crate.

Starting from rest, a 6.6-kg block slides 3.3 m down a rough 36-degree incline. The coefficient of kinetic friction between the block and the incline is μk = 0.49.  Determine the net work done on the block.

A 287-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 17.1 ° below the horizontal. The coefficient of kinetic friction is 0.253. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero? Number M. Units

Use g = 9.8 m/s². A force of constant magnitude pushes a box up a vertical surface, as shown in the figure. The box moves at a constant speed. If the mass of the box is 5.5 kg, it is pushed 3.8 m vertically upward, the coefficient of friction is 0.35, and the angle 0 is 30.0°, determine the following. (a) the work done (in J) on the box by F (b) the work done (in J) on the box by the force of gravity (c) the work done (in J) on the box by the normal force (d) the increase in gravitational potential energy (in J) of the system of the box and earth as the box moves up the wall

An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.8× 104 kg, and the force causes its speed to change from 7700 to 5600m/s. (a) What is the work done by the force? (b) If the asteroid slows down over a distance of 1.4× 106 m determine the magnitude of the force.