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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 × 10-6 N when their centers are 20 cm apart. What is the mass of each?
What is the total gravitational potential energy of the three masses in FIGURE P13.36? 10.0 kg y 10.0 kg 5.0 cm 5.0 cm 20.0 cm 20.0 kg FIGURE P13.36
What is the total gravitational potential energy of the three masses in Figure P13.35? 5.0 kg 20 cm 10.0 kg 20.0 kg 10 cm FIGURE P13.35
What are the magnitude and direction of the net gravitational force on the 20.0 kg mass in FIGURE P13.36? y 10.0 kg 10.0 kg 5.0 cm 5.0 cm 20.0 cm 20.0 kg FIGURE P13.36
FIGURE P13.35 shows three masses. What are the magnitude and the direction of the net gravitational force on? (a) The 20.0 kg mass (b) The 5.0 kg mass?? Give the direction as an angle cw or ccw from
Pluto moves in a fairly elliptical orbit around the sun. Pluto’s speed at its closest approach of 4.43 × 109 km is 6.12 km/s. What is Pluto’s speed at the most distant point in its orbit, where
In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 × 1016 kg and a radius of 8.8 km.a. What is the speed of a satellite orbiting 5.0 km
a. At what height above the earth is the free-fall acceleration 10% of its value at the surface?b. What is the speed of a satellite orbiting at that height?
What are the speed and altitude of a geosynchronous satellite orbiting Mars? Mars rotates on its axis once every 24.8 hours.
An earth satellite moves in a circular orbit at a speed of 5500 m/s.What is its orbital period?
A small moon orbits its planet in a circular orbit at a speed of 7.5 km/s. It takes 28 hours to complete one full orbit. What is the mass of the planet?
A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55 earth years to complete one orbit around the star. Vega’s mass is 2.1 times the sun’s mass. What is the
A satellite orbits the sun with a period of 1.0 day. What is the radius of its orbit?
Three satellites orbit a planet of radius R, as shown in FIGURE EX13.26. Satellites S1and S3have mass m. Satellite S2has mass 2m. Satellite S1orbits in 250 minutes and the force on S1is 10,000 N.a.
You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. You have
The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5.0 earth years. What are the asteroid’s orbital radius and speed?
A binary star system has two stars, each with the same mass as our sun, separated by 1.0 × 1012 m. A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward
Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2.0 km/s.a. The first meteoroid is heading straight for earth. What is its speed of impact?b. The second misses
You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.a.
Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00
A proposed space elevator would consist of a cable stretching from the earth’s surface to a satellite, orbiting far in space, that would keep the cable taut. A motorized climber could slowly carry
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape
A rocket is launched straight up from the earth’s surface at a speed of 15,000 m/s. What is its speed when it is very far away from the earth?
What is the escape speed from Jupiter?
An astronaut on earth can throw a ball straight up to a height of 15 m. How high can he throw the ball on Mars?
Planet Z is 10,000 km in diameter. The free-fall acceleration on Planet Z is 8.0 m/s2.a. What is the mass of Planet Z?b. What is the free-fall acceleration 10,000 km above Planet Z’s north pole?
Suppose we could shrink the earth without changing its mass.At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?
A newly discovered planet has a radius twice as large as earth’s and a mass five times as large. What is the free-fall acceleration on its surface?
Saturn’s moon Titan has a mass of 1.35 × 1023 kg and a radius of 2580 km. What is the free-fall acceleration on Titan?
A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 0.0075 m/s2 less than that at sea level. What is the observatory’s altitude?
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the
What is the free-fall acceleration at the surface of (a) The moon(b) Jupiter?
The mass of Jupiter is 300 times the mass of the earth. Jupiter orbits the sun with TJupiter = 11.9 yr in an orbit with rJupiter = 5.2rearth. Suppose the earth could be moved to the distance of
a. What is the free-fall acceleration at the surface of the sun?b. What is the free-fall acceleration toward the sun at the distance of the earth?
The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?
A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm.At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?
Why is the gravitational potential energy of two masses negative?That saying “because that’s what the equation gives” is not an explanation.
Two 65 kg astronauts leave earth in a spacecraft, sitting 1.0 m apart. How far are they from the center of the earth when the gravitational force between them is as strong as the gravitational force
The free-fall acceleration at the surface of planet 1 is 20 m/s2. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2?
The International Space Station orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the International Space Station?
A space station astronaut is working outside the station as it orbits the earth. If he drops a hammer, will it fall to earth? Explain why or why not.
What is the force of attraction between a 50 kg woman and a 70 kg man sitting 1.0 m apart?
How far away from the earth must an orbiting spacecraft be for the astronauts inside to be weightless? Explain.
The centers of a 10 kg lead ball and a 100 g lead ball are separated by 10 cm.a. What gravitational force does each exert on the other?b. What is the ratio of this gravitational force to the
A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.a. What is the ratio F1/F2 of the gravitational force on the first satellite to that on the second
What is the ratio of the sun’s gravitational force on the moon to the earth’s gravitational force on the moon?
The gravitational force of a star on orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2. What
What is the ratio of the sun’s gravitational force on you to the earth’s gravitational force on you?
Is the earth’s gravitational force on the sun larger than, smaller than, or equal to the sun’s gravitational force on the earth? Explain.
A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very bottom tip of
FIGURE CP12.89 shows a cube of mass m sliding without friction at speed v0. It undergoes a perfectly elastic collision with the bottom tip of a rod of length d and mass M = 2m. The rod is pivoted
In FIGURE CP12.88, a 200 g toy car is placed on a narrow 60-cm-diameter track with wheel grooves that keep the car going in a circle. The 1.0 kg track is free to turn on a frictionless, vertical
A rod of length L and mass M has a nonuniform mass distribution.The linear mass density (mass per length) is λ = cx2, where x is measured from the center of the rod and c is a constant.a. What are
The two blocks in FIGURE CP12.86 are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts
The bunchberry flower has the fastest-moving parts ever observed in a plant. Initially, the stamens are held by the petals in a bent position, storing elastic energy like a coiled spring. When the
The earth’s rotation axis, which is tilted 23.5° from the plane of the earth’s orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth,
During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions
A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40
A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20 rpm. John runs tangent to the merry go-round at 5.0 m/s, in the
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can
A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a
A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity
A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite€™s speed at point a is 8000
The sphere of mass M and radius R in FIGURE P12.76 is rigidly attached to a thin rod of radius r that passes through the sphere at distance 1/2 R from the center. A string wrapped around the rod
The marble rolls down the track shown in FIGURE P12.75 and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it
A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table,
A thin, uniform rod of length L and mass M is placed vertically on a horizontal table. If tilted ever so slightly, the rod will fall over.a. What is the speed of the center of mass just as the rod
The 5.0 kg, 60-cm-diameter disk in FIGURE P12.72 rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the
A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would
A 750 g disk and a 760 g ring, both 15 cm in diameter, are rolling along a horizontal surface at 1.5 m/s when they encounter a 15° slope. How far up the slope does each travel before rolling back
A hollow sphere is rolling along a horizontal floor at 5.0 m/s when it comes to a 30 incline. How far up the incline does it roll before reversing direction?
Your engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. You’ve previously determined that the turbine’s moment of inertia is 2.6 kg m2. The next
A 30-cm-diameter, 1.2 kg solid turntable rotates on a 1.2-cm diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable
The 2.0 kg, 30-cm-diameter disk in Figure P12.66 is spinning at 300 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.0 s? Brake FIGURE P12.66
Blocks of mass m1and m2are connected by a massless string that passes over the pulley in Figure P12.65. The pulley turns on frictionless bearings. Mass m1slides on a horizontal, frictionless surface.
Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial
A piece of modern sculpture consists of an 8.0-m-long, 150 kg stainless steel bar passing diametrically through a 50 kg copper sphere. The center of the sphere is 2.0 m from one end of the bar.To be
A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in Figure P12.62. What is the maximum mass of the sign if the maximum tension
Your task in a science contest is to stack four identical uniform bricks, each of length L, so that the top brick is as far to the right as possible without the stack falling over. Is it possible, as
Rank in order, from largest to smallest, the angular accelerations αato αdin FIGURE Q12.10. Explain. 2F 2F 2m 2r 2r 2m b d FIGURE Q12.10
You are given the equation(s) used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem,
You are given the equation(s) used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem,
You are given the equation(s) used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem,
A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in Figure P12.60. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it
In Figure P12.59, an 80 kg construction worker sits down 2.0 m from the end of a 1450 kg steel beam to eat his lunch.What is the tension in the cable? Cable 30°7 6.0 m
A 3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the ladder can
A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a
Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3πHR2.a. What is the distance from the apex (the point) to the center of mass?b. What is the moment of inertia for
a. A disk of mass M and radius R has a hole of radius r centered on the axis. Calculate the moment of inertia of the disk.b. Confirm that your answer agrees with Table 12.2 when r = 0 and when r =
Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation about a perpendicular axis through the center. Rotation axis L L FIGURE P12.54
Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end. Confirm that your answer agrees with Table 12.2 when d = 0
What is the moment of inertia of a 2.0 kg, 20-cm-diameter disk for rotation about an axis(a) Through the center,(b) Through the edge of the disk?
Determine the moment of inertia about the axis of the object shown in FIGURE P12.51. Rod of тp т, mass M Rotation axis FIGURE P12.51
An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass? y 20 cm 30 cm FIGURE P12.50
A 300 g ball and a 600 g ball are connected by a 40-cm-long massless, rigid rod. The structure rotates about its center of mass at 100 rpm. What is its rotational kinetic energy?
A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity
A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere.The tip of the axle is placed on a support. What is the top’s precession
A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick.What is
How fast, in rpm, would a 5.0 kg, 22-cm-diameter bowling ball have to spin to have an angular momentum of 0.23 kg m2/s?
What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? 120 rpm 2.0 m FIGURE EX12.44

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