9) A simple pendulum of length L is set to oscillate in simple harmonic motion. When its potential energy is one-half its total mechanical energy, U = E/2, then which of the following is true about its velocity:
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- Problem 1. Energy Terms Determine the potential energy of the pendulum shown below. Note: The potential en- ergy should be 0 when 0 = 0, mgL when 0=1, and 2mgL when 0 = 1. /////// 8 m Q Search 99+ H1) A pendulum bob of mass 0.710 kg is suspended by a string of length 1.50 m. The bob is released from rest when the string is at 30°to the vertical. The swing is interrupted by a peg 1.00 m vertically below the support as shown below. What is the maximum angle to the vertical made by the string after it hits the peg? 1 mA particle that can move along the x-axis is part of a system with potential energy U(x) = A x 2 − B x , where A and B are positive constants. (a) Make a sketch of U(x) vs x. (b) Where are the particle’s equilibrium positions? (You may neglect the “point” where x is very large) (c) Describe how a particle would move if given small displacements from the equilibrium positions. For each of the points you identified in Part A, identify if it is a point of stable or unstable equilibrium.
- A mass of 4.0 kg traveling at 5.0 m/s along a smooth, horizontal plane hits a relaxed spring. The mass is slowed to zero velocity when the spring has been compressed by 0.18 m. What is the final spring force when the mass is stopped?One end of a horizontal spring with k=80N/m is fixed on the wall. A 5kg block is moving at 2m/s when it touches on the free end of a spring. Find the maximum compression of spring Δ: a) if the floor is frictionless ... Δa=...b) if there is kinetic friction with magnitude 10N between block and the floor..... Δb=...c) the amount of thermal energy produced in case (a).. ΔEth-a=.... and (b)... ΔEth-b=.......OK, once again we have a pendulum, this time of length 1.86 m, which you release from rest at an angle of 52.5 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 10.5 degrees above the vertical? 3.78 m/s 0.78 m/s 5.67 m/s 3.70 m/s
- A 0.20 kg mass is attached to a spring with a spring constant equal to 240 N/m, and this mass-spring system is oscillating on a horizontal surface that is nearly frictionless. The spring was originally stretched a distance of 0.12 meters from its equilibrium (unstretched) length. a) How much did the potential energy of this mass-spring system change when the spring was originally stretched 0.12 meters? b) What is the maximum speed the mass will attain in its oscillation? c) Where in the motion is this maximum speed attained? d) What is the frequency of oscillation of this mass-spring system?OK, once again we have a pendulum, this time of length 1.18 m, which you release from rest at an angle of 46.8 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 37.4 degrees above the vertical? 3.51 m/s 1.59 m/s 2.70 m/s 2.18 m/s