Physics
7th Edition
ISBN: 9780321733627
Author: Douglas C. Giancoli
Publisher: PEARSON
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Chapter 11, Problem 63GP
An energy-absorbing car bumper has a spring constant of 410 kN/m. Find the maximum compression of the bumper if the car, with mass 1300 kg, collides with a wall at a speed of 2.0 m/s (approximately 5 mi/h).
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Students have asked these similar questions
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2. A 4.0 kg block is moving at vo 8 m/s along a frictionless, horizontal surface
towards a spring with force constant k 400 N/m that is attached to a wall. See Figure. The
spring has negligible mass. (a) Find the maximum distance the spring will be compressed.
(b) If the spring is to compress by no more than 0.15 m, what should be the maximum value
of vo?
GO Depending on how you fall, you can break a bone easily. The
severity of the break depends on how much energy the bone
absorbs in the accident, and to evaluate this let us treat the bone as an
*68.
ideal spring. The maximum applied force of compression that one man's
thighbone can endure without breaking is 7.0 × 10ª N. The minimum
effective cross-sectional area of the bone is 4.0 × 10-4 m², its length is
0.55 m, and Young's modulus is Y = 9.4 × 10° N/m². The mass of the
man is 65 kg. He falls straight down without rotating, strikes the ground
stiff-legged on one foot, and comes to a halt without rotating. To see that
it is easy to break a thighbone when falling in this fashion, find the max-
imum distance through which his center of gravity can fall without his
breaking a bone.
A 0.200-kg block along a horizontal track has a speed of 1.60 m/s immediately before colliding with a light spring of force
constant 3.70 N/m located at the end of the track.
(a) What is the spring's maximum compression if the track is frictionless?
(b) If the track is not frictionless, would the spring's maximum compression be greater than, less than, or equal to the
value obtained in part (a)?
O greater
O less
O equal
Chapter 11 Solutions
Physics
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- 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 P16.59arrow_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 block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15arrow_forward
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- 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?arrow_forwardA light spring with spring constant 1 200 N/m is hung from an elevated support. From its lower end hangs a second light spring, which has spring constant 1 800 N/m. An object of mass 1.50 kg is hung at rest from the lower end of the second spring. (a) Find the total extension distance of the pair of springs. (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series.arrow_forwardA lightweight spring with spring constant k = 225 N/m is attached to a block of mass m1 = 4.50 kg on a frictionless, horizontal table. The blockspring system is initially in the equilibrium configuration. A second block of mass m2 = 3.00 kg is then pushed against the first block, compressing the spring by x = 15.0 cm as in Figure P16.77A. When the force on the second block is removed, the spring pushes both blocks to the right. The block m2 loses contact with the springblock 1 system when the blocks reach the equilibrium configuration of the spring (Fig. P16.77B). a. What is the subsequent speed of block 2? b. Compare the speed of block 1 when it again passes through the equilibrium position with the speed of block 2 found in part (a). 77. (a) The energy of the system initially is entirely potential energy. E0=U0=12kymax2=12(225N/m)(0.150m)2=2.53J At the equilibrium position, the total energy is the total kinetic energy of both blocks: 12(m1+m2)v2=12(4.50kg+3.00kg)v2=(3.75kg)v2=2.53J Therefore, the speed of each block is v=2.53J3.75kg=0.822m/s (b) Once the second block loses contact, the first block is moving at the speed found in part (a) at the equilibrium position. The energy 01 this spring-block 1 system is conserved, so when it returns to the equilibrium position, it will be traveling at the same speed in the opposite direction, or v=0.822m/s. FIGURE P16.77arrow_forward
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