Problems 10 and 11: A nonlinear spring has a spring force function of: F =-2x (x+2) (N) 10. What is the spring potential energy function? Answer 10: 11. The spring is positioned horizontally along a frictionless surface. A 2 kg mass is pushed against the spring. By what amount should the spring be compressed so that when the mass is released, the max velocity of the mass is 5 m/s?
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- A 2.0 kg object is acted upon by a spring force characterized by the function F=-6x, (this means k = -6N/m). The speed of the object at x=3.0 m is 8.0 m/s. Determine the positive value for x where the speed of the object will be 4.9 m/s. Hint: The work done between values of x will be 1/2kx22-1/2kx12. Set this equal to the change in kinetic energy associated with the change in speed.A mass of 0.25 kg is attached to a spring whose spring constant is k = 25 N/m. The spring is compressed 0.35 m on a frictionless surface and released from rest. At what location is the kinetic energy at a maximum, what is the amount of kinetic energy, and what is the velocity of the mass at that point?You attach your 4.58 - kg Physics for Engineers book to a horizontal spring (k = 549 N/m). You then pull the book to a distance of 6.7 cm and released it from rest. If the coefficient of kinetic friction between your book and the surface is 0.31, calculate the block's speed as it passes through its original position.
- Jasmine sat on a playground toy attached to a spring. When she sat down, the height of the toy reduced from 1.2 m to 0.95 m. Jasmine has a mass of 45 kg. What is the spring constant of the playground toy?How far, in meters, would a spring, with a spring constant of 184.8 N/m, need to be stretched in order to have an elastic potential energy of 47.7 Joules?A spring with spring constant k hangs from the ceiling. A ball of mass m is attached to the spring and allowed to come to rest. It is then pulled down a distance A and released from rest. Denote the maximum velocity of the mass as vmax. What is the total mechanical energy of the spring mass system?
- Answer parts a, b and c of the following question.7. a) You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5 cm. What should be the force constant (spring constant) of this spring? b) A very light ideal spring having a spring constant (force constant) of 8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of 3.25 m/s2. If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward? c) How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?A spring is connected on one end to a wall and the other is free to be compressed. The spring constant is 25 N/cm for the spring. A 2.0 kg mass is pressed against the spring and then released and the entire system is placed on horizontal frictionless surface. (a) How much is the spring compressed when 15.0 J of energy is stored in the spring? (10.9 cm) (b) What is the acceleration when the spring is at 1/2 the maximum compression distance? (68.5 m/s2) (c) What is the maximum speed of the mass?This problem uses the ideal spring force in one dimension. F = -kx, where x is the deviation from equilibrium, and k is the spring constant. Calculate the particle's maximum speed (vmax), with these numbers: k = 2000 N/m = 2000 kg/s2 m = 5 kg (the mass of the particle) x0 = 0.2 m (the initial position) v0 = 5 m/s (the initial velocity)
- = 2. Refer to the diagram below. A spring-loaded launcher is aimed vertically upward, and compressed 0.13 m beyond its equilibrium position, then locked into place. The spring constant is k 60000 N/m. A block of mass 2 kg is placed on the launcher. When the spring lock is released, the block is launched upward to a maximum height, H. What is this height, H, if the block loses 17 Joules of mechanical energy to air resistance (during its upward flight)? Show all calculations. пиши before launch H = ? риши after launchA 0.40 kg block can slide up and down a rough 10-m-high, 30-m-long slope. At the bottom, a stiff spring with spring constant 800 N/m is compressed 0.50 m and used to launch the block up the slope. The friction force on the block from the slope is 1.2 N. Use g = 10 m/s². Match the answers with questions. the change in spring potential energy (AUsp) A. -40 J the change in gravitational potential energy (AUg) the change in thermal energy (AEth) the change in kinetic energy (AK) B. -100 J C. -18 J D. 36 E. -36 J F. 18 J G. 24 J H. 40 J I. 100 J J. -24 J