Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 7, Problem 58P
To determine
The speed of bob as it passes through the equilibrium position.
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Chapter 7 Solutions
Physics for Scientists and Engineers, Vol. 1
Ch. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - Prob. 10P
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- Check Your Understanding Suppose the mass in Equation 8.6 is doubled while keeping the all other conditions the same. Would the maximum expansion of the spring increase, decrease, or remain the same? Would the speed at point B be larger, smaller, or the same compared to the original mass?arrow_forwardA block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?arrow_forwardA 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 P7.69arrow_forward
- 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.)arrow_forwardTrue or False: The elastic potential energy of a stretched or compressed spring is always positive.arrow_forwardA block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?arrow_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along the x-axis from x=0 to x=5 m in some time interval. What is the work done by ?arrow_forwardCheck Your Understanding Find x(t) for the mass-spring system in Example 8.11 ii the particle starts from x0=0 at t=0. what is the particle’s initial velocity?arrow_forwardJane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F, on a vine having length L and initially making an angle with the vertical (Fig. P7.81). Take D = 50.0 m, F = 110 N, L = 40.0 m, and = 50.0. (a) With what minimum speed must Jane begin her swing to just make it to the other side? (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80.0 kg.arrow_forward
- A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant vanes over its stretch [see Menz, P.G. “The Physics of Bungee Jumping.” The Physics Teacher (November 1993) 31: 483-487]. Take the length of the cord to be along the direction and define the stretch as the length of the cord minus its un-stretched length that is, (see below). Suppose a particular bungee cord has a spring constant, for of and for. (Recall that the of (Recall that the spring constant is the slope of the force versus its stretch (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch It 16.7 m? Figure 7.16 (credit modification of work by Graeme Churchard)arrow_forwardCalculate the elastic potential energy of a spring with spring constant k = 225 N/m that is (a) compressed and (b) stretched by 1.00 102 m.arrow_forwardA 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?arrow_forward
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