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physics
mechanics

Questions and Answers of Mechanics

A harmonic oscillator consists of a 0.500-kg mass attached to an ideal spring with force constant 140 N/m. Find (a) The period; (b) The frequency; (c) The angular frequency of the oscillations.
Jerk A guitar string vibrates at a frequency of 440 Hz. A point at its center moves in SHM with amplitude of 3.0 mm and a phase angle of zero. (a) Write an equation for the position of the center of
A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the spring is neither stretched nor compressed and the block is moving in the negative direction at
Repeat Exercise 13.11, but assume that at t = 0 the block has velocity -4.00 m/s and displacement +0.200 m.
An object is undergoing SHM with period 1.200 s and amplitude 0.600 m. At t = 0 the object is at x = O. How far is the object from the equilibrium position when t = 0.480 s?
Weighing Astronauts this procedure has actually been used to ''weigh'' astronauts in space. A 42.5-kg chair is attached to a spring and allowed to oscillate. When it is empty, the chair takes 1.30 s
A 0.400-kg object undergoing SHM has ax = -2.70 m/s when x = 0.300 In. What is the time for one oscillation?
On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.50 N/cm. The graph in Fig. 13.31 shows the acceleration of the glider as a function of
A 0.500-kg mass on a spring has velocity as a function of time given by v(t) = (3.60 cm/s) sin [(4.71 S-I)t - 'IT/2]. What are (a) The period; (b) The amplitude; (c) The maximum acceleration of the
A 1.50-kg mass on a spring has displacement as a function of time given by the equation x(t) = (7.40 cm)cos[(4.16 S-I)t - 2.42]. Find (a) The time for one complete vibration; (b) The force constant
An object is undergoing SHM with period 0.300 s and amplitude 6.00 cm. At t = 0 the object is instantaneously at rest at x = 6.00 cm. Calculate the time it takes the object to go from x = 6.00 cm to
A tuning fork labeled 392 Hz bas the tip of each of its two prongs vibrating with an amplitude of 0.600 mm. (a) What is the maximum speed of the tip of a prong? (b) A housefly (Muscat domestic) with
A harmonic oscillator bas angular frequency", and amplitude A (a) What are the magnitudes of the displacement and velocity when the elastic potential energy is equal to the kinetic energy? (Assume
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute (a) The maximum speed of the glider; (b) The speed of
A cheerleader waves her porn-porn in SHM with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) The maximum magnitude of the acceleration and of the velocity; (b) The acceleration and
For the situation described in part (a) of Example 13.5, what should be the value of the putty mass m so that the amplitude after the collision is one-half the original amplitude? For this value of
A 0.150-kg toy is undergoing SHM on the end of a horizontal spring with force constant k = 300 N/m. When the object is 0.0120 m from its equilibrium position, it is observed to have a speed of 0.300
You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it bas a velocity of 2.20 m/s to the right and an acceleration of 8.40
On a horizontal, frictionless table, an open-topped 5.20-kg box is attached to an ideal horizontal spring having force constant 375 N/m. inside the box is a 3.44-kg stone. The system is oscillating
Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 225 N/m. The vehicle bas a steady
A proud deep-sea fisherman hangs a 65.0-kg fish from an ideal spring having negligible mass. The fish stretches the spring 0.120 m. (a) Find the force constant of the spring. The fish is now pulled
A 175-g glide Rona horizontal, frictionless airbricks attached to a fixed ideal spring with force constant 155 N/m. At the instant you make measurements on the glider, it is moving alO.815 m/s and is
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the
A l.50-kg ball and a 2.00-kg ball are glued together with the lighter one below the heavier one. The upper ball is attached to a vertical ideal spring of force constant 165 N/m, and the system is
A uniform, solid metal disk of mass 6.50 kg and diameter 24.0 cm bangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.23 N
A certain alarm clock ticks four times each second, with each tick representing half a period. The balance wheel consists of a thin rim with radius 0.55 cm, connected to the balance staff by thin
A thin metal disk with mass 2.00 X 10-3 kg and radius 2.20 cm is attached at its center to a long fiber (Fig. 13.32). The disk, when twisted and released, oscillates with a period of1.00 s. Find the
You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. You suspend it from a wire along this axis.. The wire has a torsion constant of 0.450
The balance wheel of a watch vibrates with an angular amplitude e, angular frequency"', and phase angle'" = O. (a) Find expressions for the angular velocity d81dt and angular acceleration d 281dt2 as
For the van der Waals interaction with potential-energy function given by Eq. (13.25), show that when the magnitude of the displacement x from equilibrium (r = Ro) is small, the potential energy can
When displaced from equilibrium, the two hydrogen atoms in an H2 molecule are acted on by a restoring force F. = -kt with k = 580 N/m. Calculate the oscillation frequency of the H2 molecule. (Hint:
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50 and release it. (a) How much time does it take the pendulum bob to reach its highest speed? (b) How much time does it take
An 85.0-kg mountain climber plans to swing down, starting from rest, from a ledge using a light rope 6.50 m long. He holds one end of the rope, and the other end is tied higher up on a rock face.
A building in San Francisco has light fixtures consisting of small 2.3S-kg bulbs with shades hanging from the ceiling at the end of light thin cords 1.50 m long. If a minor earthquake occurs, bow
A Pendulum on Mars a certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s2?
An apple weighs 1.00 N. When you hang it from the end of a long spring of force constant 1.50 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing
A small sphere with mass m is attached to a mass less rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side that the rod is at an angle e from the
After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 50.0 cm. She finds that the pendulum makes 100 complete swings in 136 s. What is the value of g on this
A simple pendulum 200 m long swings through a maximum angle of 30.00 with the vertical. Calculate its period (a) Assuming small amplitude, and (b) Using the first three terms of Eq. (13.35). (c)
A 1.80-kg connecting rod from a car engine is pivoted about a horizontal knife edge as shown in Fig. 13.33. The center of gravity of the rod was located by balancing and is 0.200 m from the pivot.
We want to hang a thin hoop on a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0 s. What must the hoop's mdius be?
Show that the expression for the period of a physical pendulum reduces to that of a simple pendulum if the physical pendulum consists of a particle with mass m on the end of a mass less string of
A 180-kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. 1be period for small-angle oscillations is 0940 s. (a) What is the moment of inertia of
Two pendulums have the same dimensions (length L) and total mass (m). Pendulum A is a very small ball swinging at the end of a uniform mass less bar. In pendulum B, half the mass is in the ball and
A holiday ornament in the shape of a hollow sphere with mass M = 0.015 kg and radius R = 0.050 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the
The two pendulums shown in Fig. 13.34 each consist of a uniform solid ball of mass M supported by a mass less string, but the ball for pendulum A is very tiny while the ball for pendulum B is much
A 2.20-kg mass oscillates on a spring of force constant 250.0 N/m with a period of 0.615 s. (a) Is this system damped or not? How do you know? If it is damped, find the damping constant b. (b) Is the
An unhappy 0.300-kg rodent, moving on the end of a spring with force constant k = 2.50 N/m, is acted on by a damping force Fx = -bv x. (a) If the constant b has the value 0.900 kg/s, what is the
A 50.0-g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. Its initial displacement is 0.300 m. A damping force Fx = -bv x acts on the egg, and the amplitude of the
A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value bl> the amplitude is A, when the driving angular
A sinusoidally varying driving force is applied to a damped harmonic oscillator. (a) What are the units of the damping constant b? (b) Show that the quantity Vkm has the same units as b. (c) In terms
An experimental package and its support structure, which are to be placed on board the International Space Station act as an under damped spring-mass system with a force constant of 2.1 X 106 N/m and
SHM in a Car Engine The motion of the piston of an automobile engine (Fig. 13.35) is approximately simple harmonic.(a) If the stroke of an engine (twice the amplitude) is 0.100 m and the engine runs
Four passengers with combined mass 250 kg compress the springs of a car with worn-out shock absorbers by 4.00 cm when they get in. Model the car and passengers as a single body on a single ideal
A glider is oscillating in SHM on an air track with amplitude A, You slow it so that its amplitude is halved. What happens to its (a) Period, frequency and angular frequency; (b) Total mechanical
A child with poor table manners is sliding his 250-g dinner plate back and forth in SHM with an amplitude of 0.100 m on a horizontal surface. At a point 0.060 m away from equilibrium the speed of the
A 1.50-kg horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N/m and a 275-g metal ball is in the tray. The spring is below the tray. so it can oscillate up-and
A 10.00kg mass is traveling to the right with a speed of 2.00 m/s on a smooth horizontal surface when it collides with and sticks to a second 1O.00kg mass that is initially at rest but is attached to
A rocket is accelerating upward at 4.00 m/s2 from the launch pad on the earth. Inside a small 1.50·kg ball hangs from the ceiling by a light 1.10-m wire. If the ball is displaced 8.50° from the
A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper comer (Fig. 13.37). If it is rotated
An object with mass 0.200 kg is acted on by an elastic restoring force with force constant 10.0 N/m. (a) Graph elastic potential energy U as a function of displacement x over a range of x from -
A 2.00-kg bucket containing 10.0 kg of water is hanging from a vertical ideal spring of force constant 125 N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a
A hanging wire is 1.80 m long. When a 60.O-kg steel ball is suspended from the wire, the wire stretches by 2.00 mm. If the ball is pulled down a small additional distance and released, at what
A 5.00-kg partridge is suspended from a pear tree by an ideal spring of negligible mass. When the partridge is pulled down 0.100 m below its equilibrium position and released, it vibrates with a
A 0.0200-kg bolt moves with SHM that has amplitude of 0.240 m and a period of 1.500 s. The displacement of the bolt is +0.240 m when t = O. Compute (a) The displacement of the bolt when t = 0.500 s;
SHM of a Butcher's Scale A spring of negligible mass and force constant k = 400 N/m is hung vertically, and a 0.200-kg pan is suspended from its lower end. A butcher drops a 2.2-kg steak onto the pan
A uniform beam is suspended horizontally by two identical vertical springs that are attached between the ceiling and each end of the beam. The beam has mass 225 kg, and a 175-kg sack of gravel sits
On the planet Newtonia a simple pendulum having a bob with mass 1.25 kg and a length of 185.0 cm takes 1.42 s, when released from rest, to swing through an angle of 12.5°, where it again has zero
A 40.0-N force stretches a vertical spring 0.250 m. (a) What mass must be suspended from the spring so that the system will oscillate with a period of 1.00 s? (b) If the amplitude of the motion is
Don't Miss the Boal While on a visit to Minnesota ("Land of 10,000 Lakes''), you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500- kg boat is tied,
An interesting, though highly impractical example of oscillation is the motion of an object dropped down a hole that extends from one side of the earth, through its center, to the other side. With
Two point masses m are held in place a distance d apart. Another point mass M is midway between them. M is then displaced a small distance x perpendicular to the line connecting the two fixed masses
For a certain oscillator the net force on the body with mass m is given by F. = -ex. (a) What is the potential energy function for this oscillator if we take U = 0 at x = O? (b) One-quarter of a
Consider 1he circle of reference shown in Fig. 13.6. The x-component of the velocity of Q is the velocity of P. Compute this component, and show that the velocity of P is as given by Eq. (13.15).
Two identical atoms in a diatomic molecule vibrate as harmonic oscillators. However, their center of mass, midway between 1hem, remains at rest. (a) Show that at any instant, the moment of the atoms
An approximation for the potential energy of a KCl molecules U = A[(RJ/8r8 ) - l/r], where Ro = 2.67 X l0-l0 m and A = 2.31 X 10-28 J. m. Using this approximation: (a) Show that the radial component
Two solid cylinders connected along their common axis by a short, light rod have radius R and total mass M and rest on a horizontal tabletop. A spring with force constant k has one end attached to a
In Fig. 13.39 the upper ball is released from rest, collides with the stationary lower ball, and sticks to it. The strings are both 50.0 cm long. The upper ball has mass 2.00 kg, and it is initially
T rex Model the leg of the T. rex in Example 13.10 (Section 13.6) as two uniform rods, each 1.55 m long, joined rigidly end to end. Let the lower rod have mass M and the upper rod mass 2M. The
A slender, uniform, metal rod with mass M is pivoted with out friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the
The Silently Ringing Bell Problem a large bell is hung from a wooden beam so it can swing back and forth with negligible friction. The center of mass of the bell is 0.60 m below the pivot; the bell
Two identical thin rods, each with mass m and length L, are joined at right angles to form an L-shaped object. This object is balanced on top of a shath edge (Fig. 13.41). If the L-shaped object is
You want to construct a pendulum with a period of 4.00 s at a location where g = 9.80 mfs2. (a) What is the length of a simple pendulum having this period? (b) Suppose the pendulum must be mounted in
A uniform rod of length L oscillates through small angles about a point a distance x from its center. (a) Prove that its angular frequency is Vgx/[(L2/12) + x']. (b) Show that its maximum angular
Two springs, each with unscratched length 0.200 m, but with different force constants k, and k2 are attached to opposite ends of a block with mass m on a level, frictionless surface. The outer ends
The Effective Force Constant of 'lo Springs. 'lo springs with the same unscratched length, but different force constants k, and k2 are attached to a block with mass m on a level, frictionless
(a) What is the change T in the period of a simple pendulum when the acceleration of gravity g changes by g? (Hint: The new period T + I:J.T is obtained by substituting g + g for g: To obtain an
A spring with Mass the preceding problems in this chapter have assumed that the springs had negligible mass. But of course no spring is completely mass less. To find the effect of the spring's mass,
A uniform, 1.00-m stick hangs from a horizontal axis at one end and oscillates as a physical pendulum. An object of small dimensions and with mass equal to that of the meter stick can be clamped to
You measure the period of a physical pendulum about one pivot point to be T. Then you find another pivot point on the opposite side of the center of mass that gives the same period. The two points
Resilience in a Mechanical System a mass m is attached to one end of a massless spring with a force constant k and an unscratched length 10 the other end of the spring is free to turn about a nail
Vibration of a Covalently Bonded Molecule many diatomic (two-atom) molecules are bound together by covalent bonds that are much stronger than the van der Waals interaction. Examples include H., 0
A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall (Fig. 13.36). A second block with
How far from a very small 100-kg ball would a particle have to be placed so that the ball pulled on the particle just as hard as the earth does? Is it reasonable that you could actually set up this
W.P. Wijesundera, S.H. Vosko, and F.A. Parpia (Phys. Rev. A 51, 278 (1995)) attempted to determine the electron configuration of the ground state of lawrencium, element 103. The two contending
On a part-time job, you are asked to bring a cylindrical iron rod of length 85.8 cm and diameter 2.85 cm from a storage room to a machinist. Will you need a cart? (To answer, calculate the weight of
Miles per Kilogram the density of gasoline is 737 kg/m. If your new hybrid car gets 45.0 miles per gallon of gasoline, what is its mileage in miles per kilogram of gasoline? (See Appendix E)
You purchase a rectangular piece of metal that has clemencies 5.0 x 15.0 x 30.0 nun and mass 0.0158 kg. The seller tells you that the metal is gold. To check this, you compute the average density of
Gold Brick you win the lottery and decide to impress your friends by exhibiting a million-dollar cube of gold. At the time, gold is selling for $426.60 per troy ounce, and 1.0000 troy ounces equals
A uniform lead sphere and a uniform aluminum sphere have the same mass. What is the ratio of the radius of the aluminum sphere to the radius of the lead sphere?

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