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physics
mechanics
Questions and Answers of
Mechanics
Referring to Example 4-21, show that if a skier moves at constant speed straight down a slope of angle , then the coefficient of kinetic friction between skis and snow is μk = tan θ.
(a) Show that the minimum stopping distance for an automobile traveling on a level road at speed v is equal to v2 / (2 μsg), where μs is the coefficient of static friction between the tires and the
In the equation for static friction in Section 4-8, what is the significance of the < sign? When should you use the equals sign in the static friction equation?
An antenna loosens and becomes detached from a satellite in a circular orbit around the Earth. Describe the antenna's subsequent motion. If it will land on the Earth, describe where; if not, describe
The Sun is below us at midnight, nearly in line with the Earth's center. Are we then heavier at midnight, due to the Sun's gravitational force on us, than we are at noon? Explain.
The source of the Mississippi River is closer to the center of the Earth than is its outlet in Louisiana (because the Earth is fatter at the equator than at the poles). Explain how the Mississippi
A car rounds a curve at a steady 50 km / h. If it rounds the same curve at a steady 70 km / h, will its acceleration be any different? Explain.
People sometimes ask," What keeps a satellite up in its orbit around the Earth?" How would you respond?
A child sitting 1.20 m from the center of a merry-go-round moves with a speed of 1.10 m/s. Calculate (a) The centripetal acceleration of the child and (b) The net horizontal force exerted on the
A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.20 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. (a) Find the speed of the
How many revolutions per minute would a 25-mdiameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point?
A jet pilot takes his aircraft in a vertical loop (Fig. 5-38).(a) If the jet is moving at a speed of 840 km / h at the lowest point of the loop, determine the minimum radius of the circle so that the
A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 5-39. The circle formed by the tube has a diameter of 1.1 km. What must be
On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 55.0 kg, how hard are
A coin is placed 13.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 38.0 rpm
The design of a new road includes a straight stretch that is horizontal and flat but that suddenly dips down a steep hill at 18°. The transition should be rounded with what minimum radius so that
Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5-42). If his arms are capable of exerting a force of 1150 N on the vine, what is the maximum speed he can tolerate at
Highway curves are marked with a suggested speed. If this speed is based on what would be safe in wet weather, estimate the radius of curvature for an unbanked curve marked 50 km / h. Use Table 4-2
A pilot performs an evasive maneuver by diving vertically at 270 m / s. If he can withstand an acceleration of 8.0 g's without blacking out, at what altitude must he begin to pull his plane out of
If a curve with a radius of 95 m is properly banked for a car traveling 65 km / h, what must be the coefficient of static friction for a car not to skid when traveling at 95 km / h?
Determine the tangential and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 m / s. The car's mass is 950 kg.
A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 270 km / h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of
A particle revolves in a horizontal circle of radius 1.95 m. At a particular instant, its acceleration is 1.05 m/s2, in a direction that makes an angle of 25.0° to its direction of motion. Determine
Calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if it's mass is 1850 kg.
At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.0 m/s2. A 24.0-kg brass ball is transported to this planet. What is(a) The mass of the brass ball on the
A horizontal force of 310 N is exerted on a 2.0-kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m. Calculate the speed of the ball.
A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?
Find the net force on the Moon (mM = 7.35 Ã 1022 kg) due to the gravitational attraction of both the Earth (mE = 5.98 Ã 1024 kg) and the Sun (mS = 1.99 Ã 1030
A hypothetical planet has a mass 2.80 times that of Earth, but has the same radius. What is g near its surface?
Calculate the effective value of g, the acceleration of gravity, at(a) 6400 m,(b) 6400 km, above the Earth's surface.
What is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 45 rpm (revolutions per minute) if the wheel's diameter is 35 cm?
Four 7.5-kg spheres are located at the corners of a square of side 0.80 m. Calculate the magnitude and direction of the gravitational force exerted on one sphere by the other three.
You know your mass is 62 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 77 kg. What is the acceleration of the elevator, and in which direction?
A 12.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 185 N and breaks as the elevator accelerates. What was the elevator's minimum
A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N,
What will a spring scale read for the weight of a 58.0-kg woman in an elevator that moves?(a) Upward with constant speed 5.0 m / s,(b) Downward with constant speed 5.0 m / s,(c) With an upward
What is the apparent weight of a 75-kg astronaut 2500 km from the center of the Moon in a space vehicle?(a) Moving at constant velocity and(b) Accelerating toward the Moon at 1.8 m /s2? State
At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.70 g? Assume the spaceship's diameter is 32 m, and give your answer as the time needed for one
(a) Show that if a satellite orbits very near the surface of a planet with period T, the density (mass per unit volume) of the planet is(b) Estimate the density of the Earth, given that a satellite
How fast (in rpm) must a centrifuge rotate if a particle 7.00 cm from the axis of rotation is to experience an acceleration of 125,000 g's?
Planet A and planet B are in circular orbits around a distant star. Planet A is 7.0 times farther from the star than is planet B. What is the ratio of their speeds νA/ νB
A device for training astronauts and jet fighter pilots is designed to move the trainee in a horizontal circle of radius 11.0 m. If the force felt by the trainee is 7.45 times her own weight, how
A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 m. At the very bottom, the normal force on the driver is twice
A1050-kg car rounds a curve of radius 72 m banked at an angle of 14°. If the car is traveling at 85km / h, will a friction force be required? If so, how much and in what direction?
In a "Rotor-ride" at a carnival, people rotate in a vertical cylindrically walled "room." (See Fig. 5-47.) If the room radius is 5.5 m, and the rotation frequency 0.50 revolutions per second when the
While fishing, you get bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.75 s. What is the angle that
Consider a train that rounds a curve with a radius of 570 m at a speed of 160 km / h (approximately 100 mi / h).(a) Calculate the friction force needed on a train passenger of mass 55 kg if the track
How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 125 m at a speed of 95 km / h?
What is the maximum speed with which a 1200-kg car can round a turn of radius 90.0 m on a flat road if the coefficient of friction between tires and road is 0.65? Is this result independent of the
A hill has a height h. A child on a sled (total mass m) slides down starting from rest at the top. Does the speed at the bottom depend on the angle of the hill if(a) It is icy and there is no
The energy transformations in pole vaulting and archery are discussed in this Chapter. In a similar fashion, discuss the energy transformations related to: (a) Hitting a golf ball; (b) Serving a
List some everyday forces that are not conservative, and explain why they aren't.
1. You push very hard on a heavy desk, trying to move it. You do work on the desk: (a) Whether or not it moves, as long as you are exerting a force. (b) Only if it starts moving. (c) Only if it
1. A skier starts from rest at the top of each of the hills shown in Fig. 6-34. On which hill will the skier have the highest speed at the bottom if we ignore friction:(a), (b), (c), (d), or (e) c
1. You push a heavy crate down a ramp at a constant velocity. Only four forces act on the crate. Which force does the greatest magnitude of work on the crate? (a) The force of friction. (b) The force
1. When the speed of your car is doubled, by what factor does its kinetic energy increase? (a) √2. (b) 2. (c) 4. (d) 8. 2. A car traveling at a velocity v can stop in a minimum distance d. What
1. A bowling ball is dropped from a height h onto the center of a trampoline, which launches the ball back up into the air. How high will the ball rise? (a) Significantly less than h. (b) More than
1. A car accelerates from rest to 30 km/h. Later, on a highway it accelerates from 30 km/h to 60 km/h. Which takes more energy, going from 0 to 30, or from 30 to 60? (a) 0 to 30 km/h. (b) 30 to 60
1. Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored?(a) Both hit the ground at the same
A 75.0-kg firefighter climbs a flight of stairs 28.0 m high. How much work does he do?
A 380-kg piano slides 2.9 m down a 25° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). Determine:(a) The force exerted by the man,(b)
A grocery cart with mass of 16 kg is being pushed at constant speed up a 12° ramp by a force FP which acts at an angle of 17° below the horizontal.Find the work done by each of the forces
The force on a particle, acting along the x axis, varies as shown in Fig. 6-38. Determine the work done by this force to move the particle along the x axis:(a) From x = 0.0 to x = 10.0 m;(b) From x =
A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 6-39a). The gases thrust out from the jet's engines exert a constant force of 130 kN on the jet; the force exerted on the jet
(a) If the kinetic energy of a particle is tripled, by what factor has its speed increased?(b) If the speed of a particle is halved, by what factor does its kinetic energy change?
How much work must be done to stop a 925-kg car traveling at 95 km/h?
Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed and by what factor? Which can do the most work?
The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just "let it fall" but
A baseball (m = 145g) traveling 32 m/s moves a fielder's glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?
An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?
A 265-kg load is lifted 18.0 m vertically with an acceleration a = 0.160g by a single cable. Determine (a) The tension in the cable; (b) The net work done on the load; (c) The work done by the
By how much does the gravitational potential energy of a 54-kg pole vaulter change if her center of mass rises about 4.0 m during the jump?
A spring has a spring constant k of 88.0 N/m. How much must this spring be compressed to store 45.0 J of potential energy?
If it requires 6.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?
A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high.(a) What is the hiker's change in potential energy?(b) What is the minimum work required of the hiker?(c)
A 1.60-m-tall person lifts a 1.65-kg book off the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to(a) The ground,(b) The top of the person's head?(c) How
A novice skier, starting from rest, slides down an icy frictionless 8.0° incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?
Jane, looking for Tarzan, is running at top (5.0 m/s) speed and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your
A sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?
In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to
A 1200-kg car moving on a horizontal surface has speed u = 85 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of
A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of 4.5 m/s.(a) How fast is he going as he lands on the trampoline, 2.0 m below (Fig. 6-40)?(b) If the
A vertical spring (ignore its mass), whose spring constant is 875 N/m, is attached to a table and is compressed down by 0.160 m.(a) What upward speed can it give to a 0.380-kg ball when released?(b)
A 1200-N crate rests on the floor. How much work is required to move it at constant speed(a) 5.0 m along the floor against a friction force of 230 N,(b) 5.0 m vertically?
A cyclist intends to cycle up a 7.50° hill whose vertical height is 125 m. The pedals turn in a circle of diameter 36.0 cm. Assuming the mass of bicycle plus person is 75.0 kg,(a) Calculate how much
Two railroad cars, each of mass 66,000 kg, are traveling 85 km/h toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?
A 16.0-kg child descends a slide 2.20 m high and, starting from rest, reaches the bottom with a speed of 1.25 m/s. How much thermal energy due to friction was generated in this process?
A ski starts from rest and slides down a 28° incline 85 m long.(a) If the coefficient of friction is 0.090, what is the ski's speed at the base of the incline?(b) If the snow is level at the foot of
A 145-g baseball is dropped from a tree 12.0 m above the ground.(a) With what speed would it hit the ground if air resistance could be ignored?(b) If it actually hits the ground with a speed of 8.00
What is the minimum work needed to push a 950-kg car 710 m up along a 9.0° incline? Ignore friction.
A skier traveling 11.0 m/s reaches the foot of a steady upward 19° incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?
You drop a ball from a height of 2.0 m, and it bounces back to a height of 1.6 m. (a) What fraction of its initial energy is lost during the bounce? (b) What is the ball's speed just before and
The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 m/s or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine
How long will it take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?
(a) Show that one British horsepower (550 ft · lb/s) is equal to 746 W. (b) What is the horsepower rating of a 75-W light bulb?
Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.
An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of 35km/h what is the total force resisting the motion of the boat?
A shot-putter accelerates a 7.3-kg shot from rest to 14m/s in 1.5 s. What average power was developed?
A driver notices that her 1080-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car
How much work can a 2.0-hp motor do in 1.0 h?
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