A spherically symmetric ball of mass m and radius R is centered at the origin. A thin rod has a mass M uniformly distributed along its length L and lies along the x-axis as shown in the figure below. Determine the gravitational potential energy of the system if U = 0 at x = ∞.
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- 1.A the particle has a kinetic energy of 12 J; at point B the particle is momentarily at rest, and the potential energy of the system is 25 J; at point C the potential energy of the system is 5 J. (a)What is the potential energy of the system when the particle is at point A? (b) What is the kinetic energy of the particle at point C? Draw and Explain.In an amusement park, a car with a mass of 481 kg rolls in a track as shown below. Note that the work done by the rolling friction is not zero between the starting point and point A. If the speed of the car in point A is 21 m/s, what is the magnitude of the work done by friction between the starting point and point A? Assuming that there is no friction between points A and B, and, If the speed of the car in point A is 21 m/s, what is the magnitude of the speed of the car in point B? Assuming that there is no friction between points B and C, and, If the speed of the car in point B is 5 m/s, what is the magnitude of the speed of the car in point C?A 1100 kg roller coaster car starts at point A, then travels 155 ft at 40.0° below the horizontal to point B. (a)Taking point B to be the level where the gravitational potential energy of the car–Earth system is zero, what is the potential energy (in J) of the system when the car is at points A and B, and the change in potential energy (in J) as the coaster moves between these points? -at point A -at point B -change in potential energy J (b) Repeat part (a), setting the zero configuration with the car at point A. -at point A -at point B -change in potential energy
- a) A person is riding on a Ferris wheel of radius R. He starts at the lowest point of the wheel. When the wheel makes one complete revolution, is the net work done by the gravitational force positive, zero or negative? Do you need to know how the speed of the person changed before you can answer the question? b) Suppose the person started at the highest point of the wheel. What is the net work done by the gravitational force when he reaches the lowest point?Pilings are driven into the ground at a building site by dropping a 1950 kg object onto them. What change in gravitational potential energy does the object undergo if it is released from rest 18.0 m above the ground and ends up 1.90 m above the ground? change in gravitational potential energy: J1. A 0.20-kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone-Earth system (a) before the stone is released and (b) when it reaches the bottom of the well? (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
- The figure shows four particles, each of mass 40.0 g, that form a square with an edge length of d=0.700 m. If d is reduced to 0.100 m, what is the change in the gravitational potential energy of the four-particle system? Number i ! UnitsConsider a satellite in a circular orbit above Earth’s surface. In Chapter we will learn that the force of gravity changes only the direction of motion of a satellite in circular motion (and keeps it in a circle); it does NOT change the satellite’s speed. Work done on the satellite by the gravitational force is zero. What is your explanation?A potential energy function for a system in which a two-dimensional force acts is of the form U = 3x5y − 8x. Find the force that acts at the point (x, y). (Use the following as necessary: x and y.)
- The figure shows four particles, each of mass 40.0 g, that form a square with an edge length of d = 0.900 m. If d is reduced to 0.300 m, what is the change in the gravitational potential energy of the four-particle system? Number i Units d d îassume the object has a mass of 0.55kg. calculate the gravitational potential energy and kinetic energy of the object. add the values to get the total energy. don't forget to label the units. time (s) 0.05 height (m) 4.99 speed (M/s) 0.5A pendulum bob with a mass of 0.420 kg is attached to a 1.5 m long string as shown. As the pendulum bob swings from point A, where the angle 0 = 32.0°, to point B at the bottom of its arc, determine the change in the gravitational potential energy of the pendulum bob-earth system. 1.5 m A B