A 1.16-kg box rests atop a massless vertical spring with k = 4170 N/m that has been compressed by 14.2 cm from its equilibrium position. The box is released and leaves the spring when it reaches its equilibriumposition. What is the maximum height the box reaches above its original position?Need Help?Read ItMY NG TESASK V OUR TE ACHERPRACTTICE ANNOTHED

Answered: Image /qna-images/answer/aec3b133-0788-40b1-a24d-d35772b1fcce.jpg

A 1.16-kg box rests atop a massless vertical spring with k = 4170 N/m that has been compressed by 14.2 cm from its equilibrium position. The box is released and leaves the spring when it reaches its equilil position. What is the maximum height the box reaches above its original position?

A 1.16-kg box rests atop a massless vertical spring with k = 4170 N/m that has been compressed by 14.2 cm from its equilibrium position. The box is released and leaves the spring when it reaches its equilil position. What is the maximum height the box reaches above its original position?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 42PQ: A 1.50-kg box rests atop a massless vertical spring with k = 4250 N/m that has been compressed by...

See similar textbooks

Similar questions

A block of mass 300 g is attached to a spring of spring constant 100 N/m. The other end of the spring is attached to a support while the block rests on a smooth horizontal table and can slide freely without any friction. The block is pushed horizontally till the spring compresses by 12 cm, and then the block is released from rest. (a) How much potential energy was stored in the block-spring support system when the block was just released? (b) Determine the speed of the block when it crosses the point when the spring is neither compressed nor stretched. (c) Determine the speed of the block when it has traveled a distance of 20 cm from where it was released.
A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P7.55. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? (d) Why isnt the answer to part (c) half the answer to part (b)? Figure P7.55
A weight is connected to a spring that is suspended vertically from the ceiling. If the weight is displaced downward from its equilibrium position and released, it will oscillate up and down. (a) If air resistance is neglected, will the total mechanical energy of the system (weight plus Earth plus spring) be conserved? (b) How many forms of potential energy are there for this situation?
A spring of spring constant k lies along an incline as shown in Figure P8.27. A block of mass m is attached to the spring. The spring compresses, and the block comes to rest as shown. Find an expression for the change in the Earthblockspring systems potential energy in terms of the parameters given in the figure.
A cafeteria tray dispenser supports a stack of trays on a shelf that hangs from four identical spiral springs under tension, one near each corner of the shelf. Each tray is rectangular, 45.3 cm by 35.6 cm. 0.450 cm thick, and with mass 580 g. (a) Demonstrate that the top tray in the stack can always be at the same height above the floor, however many trays are in the dispenser, (b) Find the spring constant each spring should have for the dispenser to function in this convenient way. (c) Is any piece of data unnecessary for this determination?
A childs pogo stick (Fig. P7.69) stores energy in a spring with a force constant of 2.50 104 N/m. At position (x = 0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position (x = 0), the spring is relaxed and the child is moving upward. At position , the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so lets assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the childstickEarth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine x. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Calculate the childs maximum upward speed. Figure P7.69
An archer pulls her bowstring back 0.400 m by exerting a force that increases uniformly from zero to 230 N. (a) What is the equivalent spring constant of the bow? (b) How much work does the archer do in pulling the bow? Figure P5.64
Consider the data for a block of mass m = 0.250 kg given in Table P16.59. Friction is negligible. a. What is the mechanical energy of the blockspring system? b. Write expressions for the kinetic and potential energies as functions of time. c. Plot the kinetic energy, potential energy, and mechanical energy as functions of time on the same set of axes. Problems 5965 are grouped. 59. G Table P16.59 gives the position of a block connected to a horizontal spring at several times. Sketch a motion diagram for the block. Table P16.59
An automobile having a mass of 1.00 103 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 5.00 105 N/m and is compressed 3.16 cm as the car is brought to rest. What was the speed of the car before impact, assuming no energy is lost in the collision with the wall?
A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m. (a) What is the spring constant? (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? (d) What is the speed of the block when its displacement is 0.160 m? (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.240 m on a rough surface so that it loses 14.0 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?
A 75.0-kg firefighter slides down a pole while a constant friction force of 300 N retards her motion. A horizontal 20.0-kg platform is supported by a spring at the bottom of the pole to cushion the fall. The firefighter starts from rest 4.00 m above the platform, and the spring constant is 4 000 N/m. Find (a) the firefighters speed just before she collides with the platform and (b) the maximum distance the spring is compressed. Assume the friction force acts during the entire motion.
A pendulum, comprising a light string of length L and a small sphere, swings in the vertical plane. The string hits a peg located a distance d below the point of suspension (Fig. P8.40). (a) Show that if the sphere is released from a height below that of the peg, it will return to this height after the string strikes the peg. (b) Show that if the pendulum is released from rest at the horizontal position ( = 90) and is to swing in a complete circle centered on the peg, the minimum value of d must be 3L/5. Figure P8.40