A 0.33 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k whose other end is fixed. The ladle has a kinetic energy of 62 J as it passes through its equilibrium position (the point at which the spring force is zero). (a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position? (b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position? = 320 N/m)

A 0.33 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k whose other end is fixed. The ladle has a kinetic energy of 62 J as it passes through its equilibrium position (the point at which the spring force is zero). (a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position? (b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position? = 320 N/m)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter9: Energy In Nonisolated Systems

Section: Chapter Questions

Problem 28PQ

See similar textbooks

Similar questions

As a simple pendulum swings back and forth, the forces acting on the suspended object are the force of gravity, the tension in the supporting cord, and air resistance, (a) Which of these forces, if any, does no work on the pendulum? (b) Which of these forces does negative work at all times during the pendulums motion? (c) Describe the work done by the force of gravity while the pendulum is swinging.
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 particle of mass m = 1.18 kg is attached between two identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is F=2kx(1Lx2+L2)i (b) Show that the potential energy of the system is U(x)=kx2+2kL(Lx2+L2) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the panicle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Figure P7.50
The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure P5.39b. Figure P5.39
A block on a frictionless, horizontal surface is attached to two springs as shown in Figure P8.28. The block is displaced, compressing one spring and stretching the other. a. Find an expression for the change in the blocksprings systems potential energy in terms of the parameters given in the figure. b. Is it possible to displace the block in such a way that the systems potential energy does not change? FIGURE P8.28
A jack-in-the-box is actually a system that consists of an object attached to the top of a vertical spring (Fig. P8.50). a. Sketch the energy graph for the potential energy and the total energy of the springobject system as a function of compression distance x from x = xmax to x = 0, where xmax is the maximum amount of compression of the spring. Ignore the change in gravitational potential energy. b. Sketch the kinetic energy of the system between these points the two distances in part (a)on the same graph (using a different color). FIGURE P8.50 Problems 50 and 79
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.
For each of the situations given, state whether frictional forces do positive, negative, or zero work on the italicized object. (a) A plate slides across a table and is brought to rest by friction. (b) A person pushes a chair at constant speed across a rough, horizontal surface. (c) A box is set down on a stationary conveyor belt. The conveyor belt is then turned on and the box begins to move, being carried along by the belt. (d) A person exerts a horizontal force on a banana at rest on a counter top. The banana remains at rest.
A small object is attached to two springs of the same length l, but with different spring constants k1 and k2 as shown in Figure P9.31. Initially, both springs are relaxed. The object is then displaced straight along the x axis from xi to xf. Find an expression for the work done by the springs on the object.
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
Rubber tends to be nonlinear as an elastic material. Suppose a particular rubber band exerts a restoring force given by Fx(x) = Ax Bx2, where the empirical constants are A = 14 N/m and B = 3.3 N/m2 so that Fx is in newtons when x is in meters. Calculate the change in elastic potential energy of the rubber band when an external force stretches it from x = 0 to x = 0.20 m.
A particle moves along the xaxis from x = 12.8 m to x = 23.7 m under the influence of a force F=375x3+3.75x where F is in newtons and x is in meters. Using numerical integration, determine the work done by this force on the particle during this displacement. Your result should he accurate to within 2%.