Problem 2 Consider the elastic pendulum shown in the figure below.The pendulum con- sists of a bob of mass m, connected to a spring of spring constant k Let lo be the length of the spring at equilibrium, and r be the elongation. The bob is free to move in 3D. 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions)
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- Please help me Problem 1answer this show full stepsTo test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical mass isdropped onto the mat from a height of 1 m above the mat. During the impact, the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to only 4 cm thick. a. How much kinetic energy does the cylinder have at the instant just before it contacts the mat? b. What average vertical force does the mat exert on the cylinder during the impact, from contact until the cylinder’s vertical velocity is zero?
- Two objects of different mass start from rest and are pulled horizontally with negligible friction by the same magnitude net force and moved through the same distance. The work done on object 1 is 4000 joules. After the force has pulled each object, object 1 is seen to move with half the speed of object 2. Answer the following questions and show your work. a. How much work is done on object 2? What is the kinetic energy of object 1 after being pulled? Explain. b. What is the kinetic energy of object 2 after being pulled? Explain. с.At the instant shown in the figure, the 36-N box is moving up the smooth inclined surface at 2.6 m/s. How fast will the box be moving when it has moved 1.1 m up the surface from its present position? Use the principle of work and energy and F=15.25 N. F 20° Note: Draw the necessary diagram/s before formulating any equation.Use the diagram to answer the questions A simple pendulum is suspended from the ceiling by means of a string of length 1.92 m. Assume that there is no friction or air resistance. Suppose you were to release the pendulum from rest, starting from an angle of 44.7 degrees with respect to the vertical, as shown. What will be the speed of the pendulum at the instant it swings through its lowest point (that is, when it s momentarily hanging vertically)? a. 3.30 m/s b. 5.17 m/s c. 6.14 m/s d. 1.98 m/s OK, once again we have a pendulum, this time of length 1.18 m, which you release from rest at an angle of 32.3 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 19.4 degrees above the vertical? a. 1.51 m/s b. 1.89 m/s c. 1.15 m/s d. 2.84 m/s
- A ball weighing 0.2 kg rolls along the ground. It has a speed of 3 m/s. (Eventually, it rolls up the hill shown below) a. Calculate the total energy of the ball. Show your work. b. At its highest point on the hill, the ball as at a height of 0.1 m above the ground. Is energy conserved for the ball? Either way, explain how you know.Please include explanations and work for the problems. Please write it out to make it easy to understand.Two objects of different mass start from rest and are pulled horizontally with negligible friction by the same magnitude net force and moved through the same distance. The work done on object 1 is 4000 joules. After the force has pulled each object, object 1 is seen to move with half the speed of object 2. Answer the following questions and show your work. a. How much work is done on object 2? b. What is the kinetic energy of object 1 after being pulled? Explain. C. What is the kinetic energy of object 2 after being pulled? Explain. d. What is the ratio of the mass of object 1 to the mass of object 2? Explain and show work.