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A crate on rollers is being pushed without frictional loss of energy across the floor of a freight car (see the following figure). The car is moving to the right with a constant speed v0. If the crate starts at rest relative to the freight car, then from the work-energy theorem, Fd = mv2 /2, where d, the distance the crate moves, and v, the speed of the crate, are both measured relative to the freight car. (a) To an observer at rest beside the tracks, what distance d′ is the crate pushed when it moves the distance d in the car? (b) What are the crate’s initial and final speeds v0 ′ and v′ as measured by the observer beside the tracks? (c) Show that Fd′ = m(v′)2 /2 − m(v′0)2 /2 and, consequently, that work is equal to the change in kinetic energy in both reference systems.
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- You are loading a refrigerator weighing 2135 N onto a truck, using a wheeled cart. The refrigerator is raised 1.06 m to the truck bed when it is rolled up a ramp. (Assume that there is no frictional force between the refrigerator and the ramp.) (a) Calculate the minimum work that must be done by the force you apply and the magnitude of the force if the ramp is at an angle with the horizontal of 45.0 degrees. minimum work = force = (b) Calculate the minimum work that must be done by the force you apply and the magnitude of the force if the ramp is at an angle with the horizontal of 10.2 degrees. minimum work = force=a crate with mass m = 23.9 kg being pushed up an incline that makes an angle φ = 19.2 degrees with horizontal. The pushing force is horizontal, with magnitude P, and the coefficient of kinetic friction between the crate and the incline is μ = 0.337. Consider the work done on the crate as it moves a distance d = 4.34 m at constant speed. Part (a) What is work done by the pushing force, in joules? Part (b) What is the work done by friction, in joules? Part (c) What is the work done by gravity, in joules? Part (d) What is the net work, in joules?A block of mass ?=0.350kg is released from rest, from a curved ramp of height h= 42.0 cm (point A in the figure). The block slides down frictionless to the bottom of the ramp to point B. a) What is work done by gravity when the block moves from A to B? b) What is the speed of the block at the bottom of the ramps (point B in the figure)? c) The box continuesto slide frictionless and compress a spring a distance Δ?=8.20cm until it stops at point C. What is the spring constant k of the spring? d)What is the elastic potential energy stored in the spring when the block is at point C?
- A single conservative force acts on the a 5.0 kg object. The equation Fx = 2x + 4 describes the force, where x is in meters. As the object moves along the x axis from x = 1.0 m to x = 5.0 m calculate the work done by this force.A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop). What is the child's final speed, vf in m/s?A 10 kg barbell is rolling down a hill. There is no friction or air resistance acting on it, only the force of gravity. If it starts out moving 2 ms1, and ends up moving 7 ms1, then how much work does gravity do on it?
- A car with a mass of 2000 kg starts at rest from a point 30 m above the ground. At point B, it is 15 m above the ground. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 20 000 J, what is the kinetic energy of the car at point B? (g= 10 m/s2).An object is moved on a horizontal surface by a force of 15 N up to a distance of 10 m. The force of kinetic friction is 7.5 N. What is the work done by the resultant force?You go for a walk one afternoon down a level street to a park where there is a hill. If the hill is 62 meters above street level and 4.6 km from home , how much work in the physics sense do you do in order to get to the top of the hill? Assume your mass is 65 kg and the acceleration of gravity is 9.8 m/s. Give your answer in joules (J).
- You and your friend Gandalf are mowing lawns for extra spending money. Gandalf pushes his mower 25 m and applies a force of 150 N. If you apply a force of 60 N, how far must you push your mower so that the work you do equal Gandalf’s?A horizontal force of magnitude 37.4 N pushes a block of mass 3.83 kg across a floor where the coefficient of kinetic friction is 0.639. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 3.86 m across the floor? (b) During that displacement, the thermal energy of the block increases by 39.5 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number Units (b) Number i Units (c) Number Units >The force required to compress a non-standard spring varies as the spring is compressed, as shown by the plot of force vs displacement. Distances are x1 = 10, x2 = 25 cm, x3 = 55 cm, and x4=75cm, and the forces are F1 = 110 N and F2 = -60N. Calculate the work done in Joules, on the spring as it is compressed from origin to point x4.