This time, the pendulum is 1.51 m long and has a mass of 3.01 kg. You give it a push away from vertical so that it starts swinging with a speed of 2.25 m/s. Due to friction at the pivot point, 1.00 Joule of the pendulum s initial kinetic energy is lost as heat during the upward swing. What maximum angle will it reach, with respect to the vertical, before falling back down? 1 44.2 degrees 39.1 degrees 31.6 degrees 4 34.0 degrees

9. A helium balloon is released from the floor in a room at rest, then slowly rises and comes to rest touching the ceiling. During this process, the gravitational potential energy of the balloon has increased. Since energy is conserved, the energy of something else must have decreased during this process. Which of the following is the main contribution to this decrease? (A) The kinetic energy of the balloon decreased. (B) The elastic potential energy of the balloon decreased. (C) The thermal energy of the air in the balloon decreased. (D) The thermal energy of the air in the room decreased. (E) The gravitational potential energy of the air in the room decreased. 10. An archer takes aim at a target that is 100 m away. Assuming she holds the bow at the same height as the center of the target and shoots an arrow with velocity v = 100 m/s, at what angle above the horizontal should she aim the bow so that the arrow hits the center of the target? (A) arccos (1/5) 2 (B) arcsin (1/5) 2 (C)…

In the winter activity of tubing, riders slide down snow covered slopes while sitting on large inflated rubber tubes. To get to the top of the slope, a 2.50 kg tube, is pulled at a constant speed by a tow rope that maintains a constant tension of 12.0 N along the direction of the slope. How much thermal energy is created in the slope and the tube during the ascent of a 6.10-m-high, 51.8-m-long slope, in Joule? Use g = 10.0 m/s2. Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U ( x ) = a x 3 − b x                  a)  Find the two equilibrium positions of the particle.                  b)  For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.