15. A child with a weight of 400 N sits in a playground swing. The swing is attached to a pair of ropes, each with a length of 2 m. As the child swings, she follows a circular path. At her lowest point, when the ropes are perfectly vertical, the child is at a height of 0.5 m above the ground. Let us use the ground as our reference point for gravitational potential energy. Calculate the gravitational potential energy of the child-Earth system, relative to the ground, when the ropes make an angle of 30° relative to the vertical.
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- D. E. ans: E 53. The potential energy of a 0.20-kg particle moving along the axis is given by U(z) = (8.0 J/m²)x² + (2.0J/m*)x . When the particle is at x = 1.0 m the magnitude of its acceleration is: UCI) = 10 W= -lo -lo-ma d A. 0 B. -8m/s C. 8m/s D. -40m/s E. 40 m/s ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERa radio tower is 630 m tall. A bird lands on top of the tower, so that the gravitational potential associated with the bird is 2034 J. What is the bird's mass, in kilograms? If the bird flies upward so that it reaches a maximum height of 700 m above the ground, then descends to a rooftop 22 m above ground level, what is the bird's change in gravitational potential energy in moving from its initial position on the tower to the rooftop? Assume y=0 at ground level for ths problem.1. 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?
- A 563 kg rollercoaster car starts at rest atop a 38-meter hill. Find the gravitational potential energy, when it goes over the second hill which is 14 meters high. You may assume the track is frictionless and that air resistance is negligible. 38 m 14 mA roller coaster of mass 80.0 kg is moving with a speed of 12.0 m/s at position A as shown in the figure. The vertical height above ground level at position A is 10.0 m. Neglect friction. 10 m 7 m - Potential Energy 0 What is the total mechanical energy of the roller coaster at point A? 5760 J 2080 J 37000 J 7840 J Page 18 of 30 13600 JA 6.50 kg ball hangs from the end of a 1.75 m rope. The ball is pulled back until the rope makes a 45 degrees angle with the vertical. What is the gravitational potential energy of the system? 32.49 J 52 J 78.82 J 111.48 J 16. A 16500 kg car travels at a speed of 12.5 m/s. What is its kinetic energy? 130000 J 1289062.50 J 1003125 J 206250 J 16000 J
- A horizontal spring with a spring constant k = 126 kN/m is relaxed from an extension x = 9.3 cm back to its unstretched length. Calculate the change in potential energy in Joules to 2 s.f. Your Answer: Answer10. A 0.58-kg ball is thrown vertically upward with an initial speed of 13.5 m/s. What is the potential energy of the ball when it has travelled three-quarters of the distance to its maximum height? (Use reference point of measurements of the heights) 50 ssr sf60 ss sf60 s 60 091SA child with a weight of 230 N swings on a playground swing attached to 1.80-m-long chains. What is the gravitational potential energy of the child-Earth system relative to the child's lowest position at the following times? (a) when the chains are horizontal (b) when the chains make an angle of 27.0° with respect to the vertical (c) when the child is at his lowest position
- 1. So imagine a wombat named Horace at rest. It's somehow on the top of a long telephone pole. It has a mass of 44.0 kg. It then slides down the pole reaching a final speed of 5.95 m/s just before reaching the bottom 12.4 later. (a) Calculate the change in the gravitational potential energy of Horace from top to bottom. (b) What is Horace's kinetic energy just before reaching the bottom? (c) What is the average force of friction that acts on Horace while sliding?Below is the potential energy diagram for a 50 gram particle. If the particle's mechanical energy is 7J: 10 U (1) 9 8 7 6 5 4 3 2 1 0 1 2 3 4 6 7 8 9 10 11 12 x (cm) A. Draw a line corresponding to the total Energy on the diagram. B. Assume the particle is moving in the positive x direction. Where is the particle speeding up? C. Assume the particle is moving in the positive x direction. Where is the particle lowing down? D. Where are any turning points in the particle's motion? E. What is the particle's speed at x=5 cm? F. What is the particle's maximum kinetic energy? Where does that occur? G. Suppose the particle's energy is decreased to 4J while the particle is between positions x = 7 cm and x = 9 cm. What is the particle's new maximum speed? Where does that occur?A 2kg package is moves up along a 10 m ramp AC inclined at 15' with an initial speed of 5 m/s. Knowing that the coefficient of sliding friction between the package and the incline is 0.2, answer the following questions: 10 m B 15° d 1. What force/s do/does NOT do any work on the package as it moves along the incline? 2. What is the work done by friction on the package as it moves a distance x along the incline? 3. What is the change in the kinetic energy from A to B if at position the package becomes zero? 4. What is the change in the potential energy from A to B if at position B the velocity of the package 5. What is the maximum distance that the package will move up the incline?