Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 7, Problem 92P
To determine
The minimum value of force constant.
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A block of mass 0.250 kg is placed on top of a light vertical spring of force constant 5000 N/m and pushed downward so that the spring is compressed by 0.100 m. Afterthe block is released from rest, it travels upward and then leaves the spring. To whatmaximum height above the point of release does it rise?
A horizontal spring-mass system has low friction, spring stiffness 220 N/m, and mass 0.4 kg. The system is released with an initial compression of the spring of 10 cm and an initial speed of the mass of 3 m/s.
(a) What is the maximum stretch during the motion?
A 6kg box slides across a horizontal frictionless surface at 3m/s. If the box runs into a spring with force constant 75 N/m, what is the maximum distance the spring compresses?
Chapter 7 Solutions
Physics for Scientists and Engineers
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- Consider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm. Find the speed of the block as it crosses (a) the point when the spring is not stretched, (b) 5.00 cm to the left of point in (a), and (c) 5.00 cm to the right of point in (a).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_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
- An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?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_forwardWhen a 4.00-kg object is hung vertically on a certain light spring that obeys Hookes law, the spring stretches 2.50 cm. If the 4.00-kg object is removed, (a) how far will the spring stretch if a 1.50-kg block is hung on it? (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position?arrow_forward
- At 220 m, the bungee jump at the Verzasca Dam in Locarno, Switzerland, is one of the highest jumps on record. The length of the elastic cord, which can be modeled as having negligible mass and obeying Hookes law, has to be precisely tailored to each jumper because the margin of error at the bottom of the dam is less than 10.0 m. Kristin prepares for her jump by first hanging at rest from a 10.0-m length of the cord and is observed to stretch the rope to a total length of 12.5 m. a. What length of cord should Kristin use for her jump to be exactly 220 m? b. What is the maximum acceleration she will experience during her jump?arrow_forwardCheck 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_forwardCheck Your Understanding When the length of the spring in Example 8.3 changes from an initial value of 22.0 cm to a final value, the elastic potential energy it contributes changes by 0.0800 J. Find the final length.arrow_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_forwardA block of mass 0.245 kg is placed on top of a light, vertical spring of force constant 4 800 N/m and pushed down so that the spring is compressed by 0.099 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 2-kg box, moving along a horizontal frictionless surface, hits a spring (k = 5200 N/m) on the other end at a speed of 10 m/s. How long the spring is compressed when the box brought to rest?arrow_forward
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