A bead of mass m sits on a frictionless helical wire whose shape is given by x = 4 cos(8), 4 cos(0), y = 4 sin(0), z = -50. After the bead is released from rest at z = 0 it slides down due to the gravitational force Fg = -mg k. n b) What is the energy before it is released? E = m a) Denoting the speed of the bead as u, give the formula for the energy of this bead. E= -z = 0 V= c) Give the speed of the bead when it has rotated about the z- axis n times:

A 260 g particle in a semi-spherical bowl of radius 0.6 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2 m/s. The acceleration of gravity is 9.8 m/s2 . a)What is its kinetic energy at B? b)What is the magnitude of the energy lost due to friction as the particle moves from A to B?

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 = ∞. y L M т

Constructed Response 1 Jim is lying on his back on the ground throwing a ball in the air and catching it. There is a balcony 10 meters above his head onto which he is trying to land the ball. On his last throw the ball lands on the balcony. The graph below shows the potential and kinetic energy of the ball from when it left Jim's hand to when it landed on the balcony. ★ Graivational Potential energy A Kinetic energy 200 180 160 140 120 100 80 60 40 20 0. 0. 4 9. 10 Height (m) 8. 2. Energy (J)

5 of 18 A 4500 kg spacecraft is in a circular orbit 1500 km above the I Review I Constants surface of Mars (mM = 6.42 x 1023 kg, RM = 3.39 x 10 m). Part A How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4500 km above the surface? Express your answer with the appropriate units. HẢ ? w - 1.49 • 1010 J %3D Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Provide Feedback Next > MacBook Air esc 80 DII DD F1 F2 F3 F4 FS F6 F7 FB F9 F10 F11 F12 @ # $ & * 1 2 3 4 7 9. delete Q W E R T Y 一 P

A camera weighing 15 N falls from a small drone hovering 35 m overhead and enters free fall. What is the gravitational potential energy change of the camera from the drone to the ground if you take a reference point of a. the ground being zero gravitational potential energy? APE b. The drone being zero gravitational potential energy? APE What is the gravitational potential energy of the camera (with the reference point of zero gravitational potential energy taken to be a second person looking out of a building 30 m from the ground) c. before it falls from the drone? PE=| d. after the camera lands on the ground? PE Submit Question

A particle of mass m = 1.50 kg moves along one dimension and is subject to a single force, whose potential energy function is given by U(x) = x4 – 2x2 + 4 (where U is measured in Joules and x is measured in meters). At the moment when the particle is located at position x = 1.50 m, its speed is v = 2.50 m/s. %3D

What is the best description of gravitational potential energy? a. The energy stored, dependent on the object's height from the ground. b. The strength from a moving object. c. The energy exerted through stretching or squashing an object. d. The strength stored between molecules, in chemical bonds.

m. m A mass m, = 4.1 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m, = 3 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.83 m. 1) How much work is done by gravity on the two block system? 2) How much work is done by the normal force on m,? 3) What is the final speed of the two blocks? 4) How much work is done by tension on m,? 5) What is the tension in the string as the block falls? 6) The work done by tension on only m, is: O posítive zero negative

1. A roller-coaster car with a mass of 1200 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. [Express your answers in kilojoules (kJ).] a. What is the initial potential energy of the car? b. What is the potential energy at point B? c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40 000 J (40 kJ), what is the kinetic energy of the car at point B 2. The time required for one complete cycle of a mass oscillating at the end of a spring is 0.80 s. What is the frequency of oscillation?