Problem 2 Consider the elastie 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 la 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) y
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- Please answer part D of this problem, Make sure you do the right work please and provide the right answer. DO not type your work upload a picture of your work please.A student releases the 4kg bob of a 1.92m long pendulum from the position shown. Neglect loss. What is the pendulum's height (h) above its lowest point? unit What is the pendulum's maximum speed during the swing? unit What is the tension in the string at the lowest point? unit C 27°Please include detailed explanations and work. Please write out answers and steps to make them 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.Problem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let la be the length of the spring at equili brium, and r be the elongation. The block oscillates and at the same time is rotating around origin 0, in the plane of the inclined, by a variable angular velocity . 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) k reference plane m o'HOMEWORK PROBLEMS FOR WEEK # 11 PROBLEM 1: Two SPRINGS AND A MASS k2 Con si der the sy stem shown in the diagram, which consi st s of two springs with constants k1 and k2 and a mass m. If all surfaces are frictionless, wh at is the oscillation frequency v of the mass?
- A block attached to a 15 N/m-spring constant spring moves on a frictionless horizontal surface, its position-vs-time graph is shown below. What is the total mechanical energy of the block-spring system, in Joules? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit x (cm) 20 is needed in your answer, it is already given in the question statement. 0 -20- ਲਈ 4 6 8 –t (s)Force (N) SF-2 The force required to stretch (elongate) a spring is shown in the graph to the right. 40 a) Find the spring constant K for this spring. b) The work required to stretch the- spring an infinitesimal distance dx is given by: dWk-Fdx where F-Kx. Do the integral to find an expression for the work required to stretch the spring from elongation x, to elongation x2. c) Find the work in joules to stretch the spring 5.00cm from its unloaded length. d) Find the work in joules to stretch the spring from x=5.00cm to X2=10.00cm. 35 30 25 20 15 10 0. 0 1 2 3. 4 6. 7 9 10 (cm) Spring Elongation, x Cip 45 立Loop the Loop (Figure 1)A roller coaster car may be approximated by a block of mass m. The car, which starts from rest, is released at a height h above the ground and slides along a frictionless track. The car encounters a loop of radius R, as shown. Assume that the initial height h is great enough so that the car never loses contact with the track Part A Find an expression for the kinetic energy of the car at the top of the loop. Express the kinetic energy in terms of m, g, h, and R. • View Available Hint(s) V ΑΣφ K = Submit Part B Find the minimum initial height h at which the car can be released that still allows the car to stay in contact with the track at the top of the loop. Express the minimum height in terms of R. • View Available Hint(s) Hνα ΑΣφ hmin = Submit Provide Feedback Figure < 1 of 1 h I=
- A 20kg block starts from rest and slides 6m down an incline as shown below. The block then hits a spring that has a force constant of 200 N/m. The angle of the incline is 30° and there is a coefficient of kinetic friction equal to 0.2 between the block and the incline. HK = 0.2 6m K = 200N/m www 300 Answer the following questions on your own paper and staple it to this sheet. 1. What is the speed of the block as it hits the spring? 2. At what distance from the top does the maximum speed occur? 3. What is the maximum speed of the block? 4. What is the total distance that the spring gets compressed? The spring recoils to push the block back up the incline. 5. What will be the speed of the block when it leaves the spring? 6. How far up the incline will the block travel? (above the spring)Using the principles of energy and conservation of energy, determine how the velocity of an object at the bottom of a ramp is related to its initial starting height. 1. If the ball is initially motionless at the top of a ramp of height h, write down expressions for the initial kinetic, potential, and total energy of the ball. 2. What expressions for the kinetic, potential, and total energy of the ball as it reaches the bottom of the ramp. 3. Using the principle of conservation of energy, what expression relates the final velocity of the ball to its initial height on the ramp.