The bob of a simple pendulum has a maximum speed of v_max = 2 m/s. What would be the bob's speed when its kinetic energy is equal to the potential energy? (K = U_ v = ?) (Take g = 10 m/s^2) O v = 2.83 m/s O v = 1.15 m/s v = 3.46 m/s v = 4 m/s O v = 1.41 m/s

The bob of a simple pendulum has a maximum speed of v_max = 2 m/s. What would be the bob's speed when its kinetic energy is equal to the potential energy? (K = U_ v = ?) (Take g = 10 m/s^2) O v = 2.83 m/s O v = 1.15 m/s v = 3.46 m/s v = 4 m/s O v = 1.41 m/s

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter4: Work And Energy

Section: Chapter Questions

Problem 1AYK: A fellow student tells you that she has both zero kinetic energy and zero potential energy. Is this...

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A fellow student tells you that she has both zero kinetic energy and zero potential energy. Is this possible? Explain.
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. P7.80). (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 P7.80
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
A small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15
Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x=0 , is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)
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
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
Check Your understanding In Example 8.1 what are the potential energies of the particle at x=1 m and x=2 m with respect to zero at x=1.5 ?verify that the difference of potential energy is still 7 J.
A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point , (c) its speed at point , and (d) its kinetic energy and the potential energy when the block is at point . Figure P7.45 Problems 45 and 46.
A block of mass m = 0.250 kg is pressed against a spring resting on the bottom of a plane inclined an angle = 45.0 to the horizontal. The spring, which has a force constant of 955 N/m, is compressed a distance of 8.00 cm, and the block is released from rest. Consider the total energy of the springblockEarth system. a. What is the total distance the block moves from its initial position if the incline is frictionless? b. What is the total distance the block moves from its initial position if the coefficient of kinetic friction between the incline and the block is 0.330?
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 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?