An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial kinetic energy is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? (G = 6.67 × 10−11 N·m2/kg2, ME = 5.97 × 1024 kg, RE = 6.37 × 106 m.)

Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin. Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2.    If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11?    If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?

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?

What mass of butter, which has a usable energy content of 6.0 Cal/g (= 6000 cal/g), would be equivalent to the change in gravitational potential energy of a 56 kg man who climbs 8.40 km? Assume that the average g for the climb is 9.80 m/s2.

Given: A shooting guard throws a basketball m = 1 kg straight up with an initial speed of v0 = 5.5 m/s. He releases the ball at shoulder height h0 = 1.95 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g.  What is the height, hm in meters?

You fly from Boston’s Logan Airport, at sea level, to Denver, altitude 1.6 km. Taking your mass as 65 kg and the zero of potential energy at Boston, what’s your gravitational potential energy (a) at the plane’s 11-km cruising altitude and (b) in Denver? I’ve completed the question and want to compare to see if it’s correct

The Elf on the Shelf has mass 0.500 kg and is sitting on a shelf some height y above the ground.The gravitational potential energy is 49.0 J? The Elf is bumped and falls off the shelf. How fast will the Elf be moving just before it strikes the ground?

The potential energy of a body of mass m is given by U = -mgx + 1/2kx^2. Determine the corresponding force (in Newtons) for the following values: m = 2kg , k = 20 N/m and x = 12 cm. (Hint: F = -dU/dx)

A 7.00-kg particle moves from the origin to position ©, having coordinates x = 6.50 m and y = 6.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos 0 = F · Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) B (х, у) x (m) (a) the purple path (o0©) (b) the red path (O®© (c) the blue path (O© (d) Your results should all be identical. Why? This answer has not been graded yet.

At NASA's Zero Gravity Research Facility in Cleveland, Ohio, experimental payloads fall freely from rest in an evacuated vertical shaft through a distance of 132 m. (a) If a particular payload has a mass of 28 kg, what is its potential energy relative to the bottom of the shaft? (b) How fast will the payload be traveling when it reaches the bottom of the shaft? Convert your answer to mph for a comparison to highway speeds.