You are given a magical spring which has an odd restoring force, F = -kx², THIS IS NOT THE TYPICAL SPRING RESTORING FORCE (remember, this is a magical, supernatural spring!) calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? c) If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity of the mass?

You are given a magical spring which has an odd restoring force, F = -kx², THIS IS NOT THE TYPICAL SPRING RESTORING FORCE (remember, this is a magical, supernatural spring!) calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? c) If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity of the mass?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A 90-gram mass is placed on a vertically oriented spring that then is stretched 0.5 meters below its equilibrium position and released. If the spring constant is 200 N/m, how fast will the mass be moving when it reaches the equilibrium position? Hint: You cannot ignore the change in gravitational potential energy in this problem. Please give your answer in units of m/s, however, do not explicitly include units when typing your answer into the answer box. Including actual units will result in your answer being incorrectly scored.
As shown in the figure below, a box of mass m = 9.60 kg is slidine across a horizontal frictionless surface with an initial speed v, = 3.40 m/s when k = 2950 N/m. encounters a spring of constant The box comes momentarily to rest after compressing the spring some amount x Determine the final compression x (in m) of the spring. 0.2 Can you write an expression for the initial kinetic energy of the box in terms of its mass and initial speed? What is the final kinetic energy of the box? How is the change in kinetic energy related to the initial and final kinetic energy? Since only conservative forces are acting on the system (box and spring) is energy conserved? How is the change in spring potential energy related to the change in kinetic energy of the box? How is the compression of the spring related to the change in potential energy of the spring and the spring constant? m
A mass is sliding on a frictionless surface with a speed v. It runs into a linear spring with a spring constant of k, which compresses from position xi to position xf. 1) Write a general expression for the force that the spring exerts on the mass, in term of k and x. Choose the initial position of the front of the spring to be xi=0. 2) Solve for the numerical value of the work done in Joules given that xi = 0, xf = 42 cm, and k = 105 N/m. 3) Evaluate W = - ∫xixf k x dx. Write an expression for the work done in terms of known variables.
A bead of mass m sits on a frictionless helical wire whose shape is given by x = 4 cos(0), y = 4 sin(0), z = -50. After the bead is released from rest at z = 0 it slides down due to the gravitational force Fg = = -mg k. b) What is the energy before it is released? E = a) Denoting the speed of the bead as u, give the formula for the energy of this bead. E= * m V= Z=0 c) Give the speed of the bead when it has rotated about the z- axis n times: Here frictionless means that there is no loss of energy due to reaction forces or air resistance.
a 10.2kg ball is shot out of a canon vertically up the spring (k=18100n/m) in the canon is compressed by 43.9cm to shoot the ball. a) what’s the max height of ball b) what is the velocity of the ball when it reaches a height of 12.5m c) if the ball loses 33% of its initial energy what Will the height of the ball be when it is at a speed of 9.21 m/s
A spring of negligible mass has force constant k = 1600 N/m. How far must the spring be compressed for 3.20 j of potential energy to be stored in it? 7) %3D a) b) The spring is placed vertically with one end on the floor. A 1.0-kg book is the droped from a height of 0.80 m above the top of the spring. Find the maximum distance the spring will be compressed. 1.0 kg h = 0.8 m
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?
Figure (a) applies to the spring in a cork gun (Figure (b)); it shows the spring force as a function of the stretch or compression of the spring. The spring is compressed by 7.00 cm and used to propel a 3.90 g cork from the gun. (a) What is the speed of the cork if it is released as the spring passes through its relaxed position? (b) Suppose, instead, that the cork sticks to the spring and stretches it 1.70 cm before separation occurs. What now is the speed of the cork at the time of release? Force (N) 0.4 0.2 -4-2 2 4 -0.2 -0.4 (a) x (cm) Compressed spring. 0 (b) Cork
3. If a block of mass m starts from rest at position 3 as shown below, with the spring of stiffness k compressed a distance Ax3, and slides across the frictionless plane X=0 what is its speed at position 2? (Hint: use conservation of energy.) Note: This problem gives no numbers, so don't put in numbers to do this problem. Of course you can on your scratch paper, if you want to, but for the work on this test, you need to leave it as an algebraic problem. а. V2 = b. If the block continues to slide up the frictionless incline, what is the height, h, at which it stops before sliding back down? h =
The return constant of a spring is 300 N/m. Over what length should it be stretched to store 80J of energy? A.) 0 cm B.) 3 cm C.) 13 cm D.) 23 cm E.) 33 cm F.) 43 cm G.) 53 cm H.) 63 cm I.) 73 cm
5. A 3.5 kg rock is on a spring launcher pointed vertically into the sky. It has a spring constant of 400 N/m and is compressed by 0.25 m. Given-35egha. What was the potential energy of the launcher before it was released? 400 N/m (K) O.25m x) P.E=2001(0.0625) PE12.57 b. What is the kinetic energy of the rock just after it was released? c. What is the maximum velocity of the rock? d. What is the gravitational potential energy of the rock at its highest point? e. How high did the rock go?
A student jumping on a trampoline reaches a maximum height of h = 0.91 mThe maximum height is measured from the surface of trampoline in its unstretched position . The student has a mass of m = 55 kg What is the student speed immediately before she reaches the trampoline after the jump in m/s If when she lands on the trampoline she stretches down d= 0.75 m ,what is the spring constant k in N/m of the trampoline