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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A pendulum is 0.80 m long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is 1.6 m/s. (a) What is the tension in the string at the bottom of the swing? (b) Explain why the tension is greater than the weight of the bob.
Convert these to radian measure: (a) 30.0°, (b) 135°, (c) 1/ 4 revolution, (d) 33.3 revolutions.
A 35.0-kg child swings on a rope with a length of 6.50 m that is hanging from a tree. At the bottom of the swing, the child is moving at a speed of 4.20 m/s. What is the tension in the rope?
A car approaches the top of a hill that is shaped like a vertical circle with a radius of 55.0 m. What is the fastest speed that the car can go over the hill without losing contact with the ground?
A child pushes a merry-go-round from rest to a final angular speed of 0.50rev/s with constant angular acceleration. In doing so, the child pushes the merry-go-round 2.0 revolutions. What is the angular acceleration of the merry-go-round?
A cyclist starts from rest and pedals so that the wheels make 8.0 revolutions in the first 5.0 s. What is the angular acceleration of the wheels (assumed constant)?
During normal operation, a computer's hard disk spins at 7200 rpm. If it takes the hard disk 4.0 s to reach this angular velocity starting from rest, what is the average angular acceleration of the hard disk in rad/s2?
Derive Eq. 5-20 from Eqs. 5-18 and 5-19. In Eq. 5-20 ∆ω = ωi ∆t + ½ α (∆t)2 In Eq. 5-18 ∆ω = ωf - ωi = α∆t In Eq. 5-19 ∆θ = 1/2(ωf + ωi) ∆t
Derive Eq. 5-21 from Eqs. 5-18 and 5-19. In Eq. 5-21 ω2f = ω2i = 2α ∆θ In Eq. 5-18 ∆ω = ωf - ωi = α∆t In Eq. 5-19 ∆θ = 1/2(ωf + ωi) ∆t
A pendulum is 0.800 m long and the bob has a mass of 1.00 kg. When the string makes an angle of Î¸ = 15.0° with the vertical, the bob is moving at 1.40 m/s. Find the tangential and radial acceleration components and the tension in the string.
A turntable reaches an angular speed of 33.3 rpm in 2.0 s, starting from rest. (a) Assuming the angular acceleration is constant, what is its magnitude? (b) How many revolutions does the turntable make during this time interval?
A wheel's angular acceleration is constant. Initially its angular velocity is zero. During the first 1.0-s time interval, it rotates through an angle of 90.0°. (a) Through what angle does it rotate during the next 1.0-s time interval? (b) Through what angle during the third 1.0-s time interval?
A car that is initially at rest moves along a circular path with a constant tangential acceleration component of 2.00 m/s2. The circular path has a radius of 50.0 m. The initial position of the car is at the far west location on the circle and the initial velocity is to the north. (a) After the
A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2π rad/s. After the disk rotates through 10 p radians, the angular speed is 7 π rad/s. (a) What is the magnitude of the angular acceleration? (b) How much time did it take for the disk to rotate through
In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance due to the few air molecules in the vacuum. If the rotor is spinning with an angular speed of 5.0 × 105 rad/s and the driving
The rotor of the Beams ultracentrifuge (Problem 53) is 20.0 cm long. For a point at the end of the rotor, find the In problem 53 In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance
If a washing machine's drum has a radius of 25 cm and spins at 4.0rev/s, what is the strength of the artificial gravity to which the clothes are subjected? Express your answer as a multiple of g.
A space station is shaped like a ring and rotates to simulate gravity. If the radius of the space station is 120 m, at what frequency must it rotate so that it simulates Earth's gravity?
A biologist is studying growth in space. He wants to simulate Earth's gravitational field, so he positions the plants on a rotating platform in the spaceship. The distance of each plant from the central axis of rotation is r = 0.20 m. What angular speed is required?
A biologist is studying plant growth and wants to simulate a gravitational field twice as strong as Earth's. She places the plants on a horizontal rotating table in her laboratory on Earth at a distance of 12.5 cm from the axis of rotation. What angular speed will give the plants an effective
Objects that are at rest relative to the Earth's surface are in circular motion due to Earth's rotation. (a) What is the radial acceleration of an object at the equator? (b) Is the object's apparent weight greater or less than its weight? Explain. (c) By what percentage does the apparent weight
An elevator cable winds on a drum of radius 90.0 cm that is connected to a motor. (a) If the elevator is moving down at 0.50 m/s, what is the angular speed of the drum? (b) If the elevator moves down 6.0 m, how many revolutions has the drum made?
A person of mass M stands on a bathroom scale inside a Ferris wheel compartment. The Ferris wheel has radius R and angular velocity ω. What is the apparent weight of the person (a) At the top (b) At the bottom?
A person rides a Ferris wheel that turns with constant angular velocity. Her weight is 520.0 N. At the top of the ride her apparent weight is 1.5 N different from her true weight. (a) Is her apparent weight at the top 521.5 N or 518.5 N? Why? (b) What is her apparent weight at the bottom of the
Objects that are at rest relative to Earth's surface are in circular motion due to Earth's rotation. What is the radial acceleration of a painting hanging in the Prado Museum in Madrid, Spain, at a latitude of 40.2° North?
A rotating flywheel slows down at a constant rate due to friction in its bearings. After 1 min, its angular velocity has diminished to 0.80 of its initial value ω. At the end of the third minute, what is the angular velocity in terms of the initial value?
The Earth rotates on its own axis once per day (24.0 h). What is the tangential speed of the summit of Mt. Kilimanjaro (elevation 5895 m above sea level), which is located approximately on the equator, due to the rotation of the Earth? The equatorial radius of Earth is 6378 km.
A high-speed dental drill is rotating at 3.14 × 104 rad/s. Through how many degrees does the drill rotate in 1.00 s?
A jogger runs counterclockwise around a path of radius 90.0 m at constant speed. He makes 1.00 revolution in 188.4 s. At t = 0, he is heading due east. (a) What is the jogger's instantaneous velocity at t = 376.8 s? (b) What is his instantaneous velocity at t = 94.2 s?
Two gears A and B are in contact. The radius of gear A is twice that of gear B.(a) When A's angular velocity is 6.00 Hz counterclockwise, what is B's angular velocity?(b) If A's radius to the tip of the teeth is 10.0 cm, what is the linear speed of a point on the tip of a gear tooth? What is the
If gear A in Problem 68 has an initial frequency of 0.955 Hz and an angular acceleration of 3.0 rad/s2, how many rotations does each gear go through in 2.0 s?
Grace is playing with her dolls and decides to give them a ride on a merry-go-round. She places one of them on an old record player turntable and sets the angular speed at 33.3 rpm. (a) What is their angular speed in rad/s? (b) If the doll is 13 cm from the center of the spinning turntable
The time to sunset can be estimated by holding out your arm, holding your fingers horizontally in front of your eyes, and counting the number of fingers that fit between the horizon and the setting Sun. (a) What is the angular speed, in radians per second, of the Sun's apparent circular motion
In the professional videotape recording system known as quadriplex, four tape heads are mounted on the circumference of a drum of radius 2.5 cm that spins at 1500 rad/s. (a) At what speed are the tape heads moving? (b) Why are moving tape heads used instead of stationary ones, as in audiotape
The Milky Way galaxy rotates about its center with a period of about 200 million yr. The Sun is 2 × 1020 m from the center of the galaxy. How fast is the Sun moving with respect to the center of the galaxy?
A small body of mass 0.50 kg is attached by a 0.50-mlong cord to a pin set into the surface of a frictionless table top. The body moves in a circle on the horizontal surface with a speed of 2.0πm/s. (a) What is the magnitude of the radial acceleration of the body? (b) What is the tension in the
Two blocks, one with mass m1 = 0.050 kg and one with mass m 2 = 0.030 kg, are connected to one another by a string. The inner block is connected to a central pole by another string as shown in the figure with r1 = 0.40 m and r2 = 0.75 m. When the blocks are spun around on a horizontal frictionless
What's the fastest way to make a U-turn at constant speed? Suppose that you need to make a 180° turn on a circular path. The minimum radius (due to the car's steering system) is 5.0 m, while the maximum (due to the width of the road) is 20.0 m. Your acceleration must never exceed 3.0 m/s2 or else
The Milky Way galaxy rotates about its center with a period of about 200 million yr. The Sun is 2 × 1020 m from the center of the galaxy. (a) What is the Sun's radial acceleration? (b) What is the net gravitational force on the Sun due to the other stars in the Milky Way?
You place a penny on a turntable at a distance of 10.0 cm from the center. The coefficient of static friction between the penny and the turntable is 0.350. The turntable's angular acceleration is 2.00rad/s2. How long after you turn on the turntable will the penny begin to slide off of the turntable?
A coin is placed on a turntable that is rotating at 33.3 rpm. If the coefficient of static friction between the coin and the turntable is 0.1, how far from the center of the turntable can the coin be placed without having it slip off?
A wheel is rotating at a rate of 2.0 revolutions every 3.0 s. Through what angle, in radians, does the wheel rotate in 1.0 s?
Grace, playing with her dolls, pretends the turntable of an old phonograph is a merry-go-round. The dolls are 12.7 cm from the central axis. She changes the setting from 33.3 rpm to 45.0 rpm. (a) For this new setting, what is the linear speed of a point on the turntable at the location of the
Your car's wheels are 65 cm in diameter and the wheels are spinning at an angular velocity of 101 rad/s. How fast is your car moving in kilometers per hour (assume no slippage)?
In an amusement park rocket ride, cars are suspended from 4.25-m cables attached to rotating arms at a distance of 6.00 m from the axis of rotation. The cables swing out at an angle of 45.0° when the ride is operating.What is the angular speed of rotation?
Centrifuges are commonly used in biological laboratories for the isolation and maintenance of cell preparations. For cell separation, the centrifugation conditions are typically 1.0 × 103 rpm using an 8.0-cm-radius rotor. (a) What is the radial acceleration of material in the centrifuge under
You take a homemade "accelerometer" to an amusement park. This accelerometer consists of a metal nut attached to a string and connected to a protractor, as shown in the figure. While riding a roller coaster that is moving at a uniform speed around a circular path, you hold up the accelerometer and
Massimo, a machinist, is cutting threads for a bolt on a lathe. He wants the bolt to have 18 threads per inch. If the cutting tool moves parallel to the axis of the would be bolt at a linear velocity of 0.080 in./s, what must the rotational speed of the lathe chuck be to ensure the correct thread
In Chapter 19 we will see that a charged particle can undergo uniform circular motion when acted on by a magnetic force and no other forces. (a) For that to be true, what must be the angle between the magnetic force and the particle's velocity? (b) The magnitude of the magnetic force on a charged
Find the orbital radius of a geosynchronous satellite. Do not assume the speed found in Example 5.9. Start by writing an equation that relates the period, radius, and speed of the orbiting satellite. Then apply Newton's second law to the satellite. You will have two equations with two unknowns (the
In the construction of railroads, it is important that curves be gentle, so as not to damage passengers or freight. Curvature is not measured by the radius of curvature, but in the following way. First a 100.0-ft-long chord is measured. Then the curvature is reported as the angle subtended by two
The graph shows the tension in a rubber band as it is first stretched and then allowed to contract. As you stretch a rubber band, the tension force at a particular length (on the way to a maximum stretch) is larger than the force at that same length as you let the rubber band contract. That is why
A 0.50-kg block, starting at rest, slides down a 30.0° incline with kinetic friction coefficient 0.25 (see the figure with Problem 63). After sliding 85 cm down the incline, it slides across a frictionless horizontal surface and encounters a spring (k = 35 N/m). (a) What is the maximum compression
A wind turbine converts some of the kinetic energy of the wind into electric energy. Suppose that the blades of a small wind turbine have length L = 4.0 m. (a) When a 10 m/s (22 mi/h) wind blows head-on, what volume of air (in m3) passes through the circular area swept out by the blades in 1.0
Use dimensional analysis to show that the electric power output of a wind turbine is proportional to the cube of the wind speed. The relevant quantities on which the power can depend are the length L of the rotor blades, the density ( of air (SI units kg/m3), and the wind speed v?
Use this method to find how the speed with which animals of similar shape can run up a hill depends on the size of the animal. Let L represent some characteristic length, such as the height or diameter of the animal. Assume that the maximum rate at which the animal can do work is proportional to
The potential energy of a particle constrained to move along the x -axis is shown in the graph. At x = 0, the particle is moving in the + x -direction with a kinetic energy of 200 J. Can this particle get into the region 3 cm
A record company executive is on his way to a TV interview and is carrying a promotional CD in his briefcase. The mass of the briefcase and its contents is 5.00 kg. The executive realizes that he is going to be late. Starting from rest, he starts to run, reaching a speed of 2.50 m/s. What is the
The potential energy of a particle constrained to move along the x -axis is shown in the graph. At x = 0, the particle is moving in the + x -direction with a kinetic energy of 400 J. Can this particle get into the region 3 cm < x < 8 cm? Explain. If it can, what is its kinetic energy in that
In 1899, Charles M. "Mile a Minute" Murphy set a record for speed on a bicycle by pedaling for a mile at an average of 62.3 mph (27.8 m/s) on a 3-mi track of plywood planks set over railroad ties in the draft of a Long Island Railroad train. In 1985, a record was set for this type of "motor pacing"
Sam pushes a 10.0-kg sack of bread flour on a frictionless horizontal surface with a constant horizontal force of 2.0 N starting from rest. (a) What is the kinetic energy of the sack after Sam has pushed it a distance of 35 cm? (b) What is the speed of the sack after Sam has pushed it a distance of
Josie and Charlotte push a 12-kg bag of playground sand for a sandbox on a frictionless, horizontal, wet polyvinyl surface with a constant, horizontal force for a distance of 8.0 m, starting from rest. If the final speed of the sand bag is 0.40 m/s, what is the magnitude of the force with which
A ball of mass 0.10 kg moving with speed of 2.0 m/s hits a wall and bounces back with the same speed in the opposite direction. What is the change in the ball's kinetic energy?
Jim rides his skateboard down a ramp that is in the shape of a quarter circle with a radius of 5.00 m. At the bottom of the ramp, Jim is moving at 9.00 m/s. Jim and his skateboard have a mass of 65.0 kg. How much work is done by friction as the skateboard goes down the ramp?
A 69.0-kg short-track ice skater is racing at a speed of 11.0 m/s when he falls down and slides across the ice into a padded wall that brings him to rest. Assuming that he doesn't lose any speed during the fall or while sliding across the ice, how much work is done by the wall while stopping the
A plane weighing 220 kN (25 tons) lands on an aircraft carrier. The plane is moving horizontally at 67 m/s (150 mi/h) when its tailhook grabs hold of the arresting cables. The cables bring the plane to a stop in a distance of 84 m.(a) How much work is done on the plane by the arresting cables?(b)
A shooting star is a meteoroid that burns up when it reaches Earth's atmosphere. Many of these meteoroids are quite small. Calculate the kinetic energy of a meteoroid of mass 5.0 g moving at a speed of 48 km/s and compare it to the kinetic energy of a 1100-kg car moving at 29 m/s (65 mi/h)?
A sled is dragged along a horizontal path at a constant speed of 1.5 m/s by a rope that is inclined at an angle of 30.0° with respect to the horizontal. The total weight of the sled is 470 N. The tension in the rope is 240 N. How much work is done by the rope on the sled in a time interval of
Sean climbs a tower that is 82.3 m high to make a jump with a parachute. The mass of Sean plus the parachute is 68.0 kg. If U = 0 at ground level, what is the potential energy of Sean and the parachute at the top of the tower?
Justin moves a desk 5.0 m across a level floor by pushing on it with a constant horizontal force of 340 N. (It slides for a negligibly small distance before coming to a stop when the force is removed.) Then, changing his mind, he moves it back to its starting point, again by pushing with a constant
An airline executive decides to economize by reducing the amount of fuel required for long-distance flights. He orders the ground crew to remove the paint from the outer surface of each plane. The paint removed from a single plane has a mass of approximately 100 kg. (a) If the airplane cruises at
Emil is tossing an orange of mass 0.30 kg into the air. (a) Emil throws the orange straight up and then catches it, throwing and catching it at the same point in space. What is the change in the potential energy of the orange during its trajectory? Ignore air resistance. (b) Emil throws the orange
A brick of mass 1.0 kg slides down an icy roof inclined at 30.0 ° with respect to the horizontal.(a) If the brick starts from rest, how fast is it moving when it reaches the edge of the roof 2.00 m away? Ignore friction.
An arrangement of two pulleys, as shown in the figure, is used to lift a 48.0-kg mass a distance of 4.00 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical. (a) What is the mechanical advantage of this system? (In other words, by
Find the work done by the movers as they slide the chest up the ramp if the coefficient of friction between the chest and the ramp is 0.20? For Information: Example 6.1,
A cart moving to the right passes point 1 at a speed of 20.0 m/s. Let g = 9.81 m/s2.(a) What is the speed of the cart as it passes point 3?(b) Will the cart reach position 4? Ignore friction.
A cart starts from position 4 with a velocity of 15 m/s to the left. Find the speed with which the cart reaches positions 1, 2, and 3. Ignore friction?
Bruce stands on a bank beside a pond, grasps the end of a 20.0-m-long rope attached to a nearby tree and swings out to drop into the water. If the rope starts at an angle of 35.0° with the vertical, what is Bruce's speed at the bottom of the swing?
The maximum speed of a child on a swing is 4.9 m/s. The child's height above the ground is 0.70 m at the lowest point in his motion. How high above the ground is he at his highest point?
If the skier of Example 6.6 is moving at 12 m/s at the bottom of the trail, calculate the total work done by friction and air resistance during the run. The skier's mass is 75 kg?
A 750-kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air resistance, what is the value of h, the
Rachel is on the roof of a building, h meters above ground. She throws a heavy ball into the air with a speed v, at an angle ( with respect to the horizontal. Ignore air resistance. (a) Find the speed of the ball when it hits the ground in terms of h, v, (, and g? (b) For what value(s) of ( is the
A crate of mass m1 on a frictionless inclined plane is attached to another crate of mass m2 by a mass less rope. The rope passes over an ideal pulley so the mass m2 is suspended in air. The plane is inclined at an angle ( = 36.9°. Use conservation of energy to find how fast crate m2 is moving
The forces required to extend a spring to various lengths are measured. The results are shown in the following table. Using the data in the table, plot a graph that helps you to answer the following two questions:(a) What is the spring constant?(b) What is the relaxed length of the spring?
A 75.0-kg skier starts from rest and slides down a 32.0-m frictionless slope that is inclined at an angle of 15.0° with the horizontal. Ignore air resistance. (a) Calculate the work done by gravity on the skier and the work done by the normal force on the skier. (b) If the slope is not
You are on the Moon and would like to send a probe into space so that it does not fall back to the surface of the Moon. What launch speed do you need?
A planet with a radius of 6.00 × 107 m has a gravitational field of magnitude 30.0 m/s2 at the surface. What is the escape speed from the planet?
The escape speed from the surface of Planet Zoroaster is 12.0 km/s. The planet has no atmosphere. A meteor far away from the planet moves at speed 5.0 km/s on a collision course with Zoroaster. How fast is the meteor going when it hits the surface of the planet?
The tension in the horizontal towrope pulling a water-skiers is 240 N while the skier moves due west a distance of 54 m. How much work does the towrope do on the water-skier?
The escape speed from the surface of the Earth is 11.2 km/s. What would be the escape speed from another planet of the same density (mass per unit volume) as Earth but with a radius twice that of Earth?
A satellite is placed in a noncircular orbit about the Earth. The farthest point of its orbit (apogee) is 4 Earth radii from the center of the Earth, while its nearest point ( perigee ) is 2 Earth radii from the Earth's center. If we define the gravitational potential energy U to be zero for an
What is the minimum speed with which a meteor strikes the top of the Earth's stratosphere (about 40 km above Earth's surface), assuming that the meteor begins as a bit of interplanetary debris far from Earth? Assume the drag force is negligible until the meteor reaches the stratosphere?
A projectile with mass of 500 kg is launched straight up from the Earth's surface with an initial speed vi. What magnitude of vi enables the projectile to just reach a maximum height of 5 RE, measured from the center of the Earth? Ignore air friction as the projectile goes through the Earth's
The orbit of Halley's comet around the Sun is a long thin ellipse. At its aphelion (point farthest from the Sun), the comet is 5.3 × 1012 m from the Sun and moves with a speed of 10.0 km/s. What is the comet's speed at its perihelion (closest approach to the Sun) where its distance from the Sun is
Suppose a satellite is in a circular orbit 3.0 Earth radii above the surface of the Earth (4.0 Earth radii from the center of the Earth). By how much does it have to increase its speed in order to be able to escape Earth? [You need to calculate the orbital speed and the escape speed.]
An asteroid hits the Moon and ejects a large rock from its surface. The rock has enough speed to travel to a point between the Earth and the Moon where the gravitational forces on it from the Earth and the Moon are equal in magnitude and opposite in direction. At that point the rock has a very
How much work is done on the bowstring of Example 6.9 to draw it back by 20.0 cm? [Rather than recalculate from scratch, use proportional reasoning.]
An ideal spring has a spring constant k = 20.0 N/m. What is the amount of work that must be done to stretch the spring 0.40 m from its relaxed length?
The force that must be exerted to drive a nail into a wall is roughly as shown in the graph. The first 1.2 cm are through soft drywall; then the nail enters the solid wooden stud. How much work must be done to hammer the nail a horizontal distance of 5.0 cm into the wall?
A barge of mass 5.0 Ã— 104 kg is pulled along the Erie Canal by two mules, walking along towpaths parallel to the canal on either side of it. The ropes harnessed to the mules make angles of 45° to the canal. Each mule is pulling on its rope with a force of 1.0 kN. How much work is

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