PHYSICS F/SCI.+ENGINEERS W/MOD.PHYSICS
5th Edition
ISBN: 9780321992277
Author: GIANCOLI
Publisher: PEARSON
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Problem 2 ( ). A very light spring with spring constant 200 N/m hangs vertically
the ceiling with equilbrium length Lo = 6 cm. When a 300 g mass is attached to the end
spring, the mass-spring system extends to a new equilibrium length.
Lo
y = 0
(a)
What is the length L of the spring when the mass-spring system is in equilibrium?
If the mass is released from rest with the spring at its original equilibrium length
(b)
6 cm, find the velocity of the mass when the spring has stretched to the length L you found in (a).
000000
A spring of natural length 30 cm is attached to the floor directly below an identical spring that isattached to the ceiling. The ceiling is at a height of 3 m above the floor. A ball of mass 3 kg andradius 5 cm is projected vertically downwards with a speed of 10 m s-1from midway between the two springs.(a) If the lower spring is compressed to a length of 10 cm when the ball first comes to rest,calculate the spring constant of the springs.(b) After bouncing off the lower spring, the ball impacts the upper spring. Calculate the lengthof the upper spring when the ball comes to rest for the second time.
A box (mass = 100 g) is initially connected to a compressed (x = 80 cm) spring (? = 100 N/m) at point A. It was released and started moving along the horizontal surface (?? = 0.2) until it moves up along the inclined surface (?? = 0.3). The box then stops at point D alone the incline. Consider that ? = 30 m and θ = 30.(d) What is the length of the incline, ?? (Ans. 34.88 m) (e) What is the change in gravitational potential energy from point A to point D? (Ans. 17.10 J) Kindly answer only d and e
Chapter 14 Solutions
PHYSICS F/SCI.+ENGINEERS W/MOD.PHYSICS
Ch. 14.1 - A mass is oscillating on a frictionless surface at...Ch. 14.1 - If an oscillating mass has a frequency of 1.25 Hz,...Ch. 14.2 - By how much should the mass on the end of a spring...Ch. 14.2 - The position of a SHO is given by x = (0.80 m)...Ch. 14.3 - Suppose the spring in Fig. 1410 is compressed to x...Ch. 14.5 - Return to the Chapter-Opening Question, p. 369,...Ch. 14.5 - If a simple pendulum is taken from sea level to...Ch. 14 - Give some examples of everyday vibrating objects....Ch. 14 - Is the acceleration of a simple harmonic...Ch. 14 - Real springs have mass. Will the true period and...
Ch. 14 - How could you double the maximum speed of a simple...Ch. 14 - A 5.0-kg trout is attached to the hook of a...Ch. 14 - If a pendulum clock is accurate at sea level, will...Ch. 14 - A tire swing hanging from a branch reaches nearly...Ch. 14 - For a simple harmonic oscillator, when (if ever)...Ch. 14 - Prob. 9QCh. 14 - Does a car bounce on its springs faster when it is...Ch. 14 - Prob. 11QCh. 14 - A thin uniform rod of mass m is suspended from one...Ch. 14 - What is the approximate period of your walking...Ch. 14 - A tuning fork of natural frequency 264 Hz sits on...Ch. 14 - Why can you make water slosh back and forth in a...Ch. 14 - Give several everyday examples of resonance.Ch. 14 - Prob. 17QCh. 14 - Over the years, buildings have been able to be...Ch. 14 - Prob. 1MCQCh. 14 - Prob. 2MCQCh. 14 - Prob. 3MCQCh. 14 - Prob. 4MCQCh. 14 - Prob. 5MCQCh. 14 - Prob. 6MCQCh. 14 - Prob. 7MCQCh. 14 - Prob. 8MCQCh. 14 - Prob. 9MCQCh. 14 - Prob. 10MCQCh. 14 - Prob. 11MCQCh. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3PCh. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - Prob. 6PCh. 14 - Prob. 7PCh. 14 - (II) Construct a Table, indicating the position x...Ch. 14 - Prob. 9PCh. 14 - Prob. 10PCh. 14 - Prob. 11PCh. 14 - (II) An object of unknown mass m is hung from a...Ch. 14 - (II) Figure 1429 shows two examples of SHM,...Ch. 14 - Prob. 14PCh. 14 - Prob. 15PCh. 14 - Prob. 16PCh. 14 - Prob. 17PCh. 14 - Prob. 18PCh. 14 - Prob. 19PCh. 14 - Prob. 20PCh. 14 - Prob. 21PCh. 14 - Prob. 22PCh. 14 - Prob. 23PCh. 14 - (III) A mass m is at rest on the end of a spring...Ch. 14 - (III) A mass m is connected to two springs, with...Ch. 14 - Prob. 26PCh. 14 - Prob. 27PCh. 14 - Prob. 28PCh. 14 - Prob. 29PCh. 14 - Prob. 30PCh. 14 - Prob. 31PCh. 14 - Prob. 32PCh. 14 - Prob. 33PCh. 14 - Prob. 34PCh. 14 - Prob. 35PCh. 14 - Prob. 36PCh. 14 - Prob. 37PCh. 14 - Prob. 38PCh. 14 - Prob. 39PCh. 14 - Prob. 40PCh. 14 - Prob. 41PCh. 14 - Prob. 42PCh. 14 - Prob. 43PCh. 14 - Prob. 44PCh. 14 - Prob. 45PCh. 14 - Prob. 46PCh. 14 - Prob. 47PCh. 14 - (II) Derive a formula for the maximum speed vmax...Ch. 14 - Prob. 49PCh. 14 - Prob. 50PCh. 14 - Prob. 51PCh. 14 - (II) (a) Determine the equation of motion (for as...Ch. 14 - (II) A meter stick is hung at its center from a...Ch. 14 - Prob. 55PCh. 14 - (II) A student wants to use a meter stick as a...Ch. 14 - (II) A plywood disk of radius 20.0cm and mass...Ch. 14 - (II) Estimate how the damping constant changes...Ch. 14 - Prob. 63PCh. 14 - Prob. 65PCh. 14 - Prob. 67PCh. 14 - (II) (a) For a forced oscillation at resonance ( =...Ch. 14 - Prob. 69PCh. 14 - (III) By direct substitution, show that Eq. 1422,...Ch. 14 - Prob. 75GPCh. 14 - Prob. 77GPCh. 14 - A 0.650-kg mass oscillates according to the...Ch. 14 - Prob. 83GPCh. 14 - An oxygen atom at a particular site within a DNA...Ch. 14 - A seconds pendulum has a period of exactly 2.000...Ch. 14 - Prob. 87GPCh. 14 - Prob. 89GPCh. 14 - Carbon dioxide is a linear molecule. The...Ch. 14 - A mass attached to the end of a spring is...Ch. 14 - Imagine that a 10-cm-diameter circular hole was...Ch. 14 - In Section 145, the oscillation of a simple...
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- A 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_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_forwardA 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_forward
- 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 P7.80arrow_forwardA simple pendulum as shown in Fig. 4.24 oscillates back and forth. Use the letter designations in the figure to identify the pendulums position(s) for the following conditions. (There may be more than one answer. Consider the pendulum to be ideal with no energy losses.) (a) Position(s) of instantaneous rest ___ (b) Position(s) of maximum velocity ___ (c) Position(s) of maximum Ek ___ (d) Position(s) of maximum Ep ___ (e) Position(s) of minimum Ek ___ (f) Position(s) of minimum Ep ___ (g) Position(s) after which Ek increases ___ (h) Position(s) after which Ep increases ___ (i) Position(s) after which Ek decreases ___ (j) Position(s) after which Ep decreases ___ Figure 4.24 The Simple Pendulum and Energyarrow_forwardConsider 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_forward
- 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 P7.69arrow_forwardA fellow student tells you that she has both zero kinetic energy and zero potential energy. Is this possible? Explain.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 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_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 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_forward
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