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physics
mechanics

Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

A train locomotive is pulling two cars of the same mass behind it, Fig, 4-47. Determine the ratio of the tension in the coupling between the locomotive and the first car (FT1), to that between the first car and the second car (FT2), for any nonzero acceleration of the train.
A window washer pulls herself upward using the bucket-pulley apparatus shown is Fig. 4.48.(a) How hard must she pull downward to raise herself slowly at constant speed?(b) If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 65kg?
At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22o angle with respect to the ground.(a) What was the horizontal acceleration of the sprinter?(b) If the force was exerted for 0.32s, with what speed did the sprinter leave the starting block?
Figure 4-49 shows a block (mass mA) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mB), which hangs vertically.(a) Draw a free-body diagram for each block showing the force of gravity on each, the force (tension) exerted by the cord, any normal
A pair of fuzzy dice is handing by a string from your rearview mirror, While you are accelerating from a stop-light to 28m/s in 6.0s, what angle θ does the string make with the vertical? See Fig. 4-50.
Three blocks on a frictionless horizontal surface are in contact with each other, as shown in Fig/ 4-51. A force F is applied to block A (mass mA).(a) Draw a free-body diagram for each block. Determine(b) The acceleration of the system (in terms of mA, mB, and mC),(c) The net force on each block,
The two masses shown in Fig. 4-52 are each initially 1.80m above the ground, and the mass less frictionless pulley is 4.8 above the ground. What maximum height does the lighter object reach after the system is released?
Suppose two boxes on a frictionless table are connected by a heavy cord of mass 1.0kg. Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume FP = 40.0N, and ignore sagging of the cord. Compare your results to Example
If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if μk is zero?
A force of 48.0N is required to start a 50-kg box moving across a horizontal concrete floor.(a) What is the coefficient of static friction between the box and the floor?(b) If the 48.0-N force continues the box accelerates at 0.70m/s2. What is the coefficient of kinetic friction?
Suppose that you are standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?
What is the maximum acceleration a car can undergo if the coefficient of static friction between the tires and ground is 0.80?
The coefficient of static friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?
A 15.0-kg box is released on a 32o incline and accelerates down the incline at 0.30 m/s2. Find the friction force impeding its motion. What is the coefficient of kinetic friction?
A car can decelerate at –4.80m/s2 without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13o uphill? Assume the same static friction coefficient.
(a) A box sits at rest on a rough 30o inclined plane. Draw the free-body diagram, showing all the acting on the box. (b) How would the diagram change if the box were sliding down the plane?(c) How would it change if the box were sliding up the plane after an initial shove?
Drag-race tires in contact with an asphalt surface have a very high coefficient of static friction. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12s starting from rest.
The coefficient of kinetic friction for a 22-kg bobsled on a track is 0.10. What force is required to push it down a 6.0o incline and achieve a speed of 60 km/h at the end of 75m?
For the system of Fig 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assume μs = 0.30
A box is given a push on that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0m/s?
Two crates, of mass 75kg and 110kg, are in contact and at rest on a horizontal surface (Fig. 4-54). A 620-N force is exerted on the 75-kg crate. If the coefficient of kinetic friction is 0.15, calculate(a) The acceleration of the system, and(b) The force that each crate exerts on the other.(c)
A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?
On an icy day, you worry about parking your car in you driveway, which has an incline of 12o. Your neighbor’s driveway has an incline of 9.0o, and the driveway across the street is at 6.0o. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to
A child slides down a slide with a 28o incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless, Calculate the coefficient of kinetic friction between the slide and the child.
The cartoon shown in Figure lies on a plane tilted at and angle θ = 22.0o to the horizontal, with μk = 0.12.(a) Determine the acceleration of the carton as it slides down the plane.(b) If the carton starts from rest 9.30m up the plane from its base, what will be the carton€™s
A carton is given an initial speed of 3.0m/s up the 22.0o Plane shown in Fig, 4-55.(a) How far up the plane will it go?(b) How much time elapses before it returns to its starting point? Ignore friction.
A roller coaster reaches the top of the steepest hill with a speed of 6.0 km/h. It then descends the hill, which is at an average angle of 45o and is 45.0m long. Estimate its speed when it reaches the bottom. Assume μk = 0.18.
An 18.0-kg box is released on a 37.0oIncline and accelerates down the incline at 0.270m/s2. Find the frication of kinetic friction?
A small box is held in place against a rough wall by someone pushing on it with a force directed upward at 28o above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30, respectively. The box slides down unless the applied force has magnitude
Piles of snow on slippery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of 30o. (a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?(b) As the snow begins to melt, the
(a) Show that the minimum stopping distance for and automobile traveling at speed v is equal to v2/2μsg, where μs is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity. (b) What is this distance for a 1200-kg car traveling 95 km/h if
A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 45km/h to rest in 3.5s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?
A small block of mass m is given and initial speed vo up a ramp inclined at angle θ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.
The 75 €“kg climber in Figure is supported in the €œchimney€ by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60, respectively. What is the
Boxes are moved on a conveyor belt from where they are filled to the packing station 11.0m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance then decelerates for the final half of the trip. If
A block (mass m1) lying on a frictionless inclined plane is connected to a mass m2 by a mass less cord passing over a pulley, as shown in Fig. 4-57.(a) Determine a formula for the acceleration of the system of the two block in terms of m1, m2, θ and g.(b) What conditions apply to masses m1
(a) Suppose the coefficient of kinetic friction between m1 and the plane in Fig. 4-57 is μk = 0.15 and that m1 = m2 = 2.7 kg. As m2 moves down, determine the magnitude of the acceleration of m1 and m2, given θ 25o. (b) What smallest value of μk will keep this system from
A bicyclist of mass 65kg (including the bicycle) can coast down a 6.0o hill at a stead speed of 6.0 km/h because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?
According to a simplified model of a mammalian heart, at each pulse approximately 20g of blood is accelerated from 0.25m/s to 0.35m/s during a period of 0.10s. What is the magnitude of the force exerted by the heart muscle?
A person has a reasonable chance of surviving and automobile crash if the deceleration is no more than 30 “g’s” calculate the force on a 70-kg person undergoing this acceleration, what distance is traveled if the person is brought to rest at this rate from 100km/h?
(a) If the horizontal acceleration produced by an earth-quake is a, and if an object is going to “hold its place” on the ground, show that the coefficient of static friction with the ground must be at least μs = 1/g. (b) The famous Loma Prieta earthquake that stopped the 1989 World Series
An 1150-kg car pulls a 450-kg trailer. The car exerts a horizontal force of 3.8 x 103 N against the ground in order to accelerate. What force does the car exert on the trailer?Assume an effective friction coefficient of 0.15 for the trailer?
Police investigators, examining the scene of and accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding the coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of the car
A car starts rolling down a 1-in-4 hill (1-in-r mean that for each 4m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55m?(a) Ignore friction.(b) Assume an effective coefficient of friction equal to 0.10.
A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55m before reaching the ground with a speed of 29m/s. What was the average force of air resistance?
A cyclist is coasting at a steady speed of 12 m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11m? If so, what will be the speed upon emerging?
A city planer is working on the redesign of a hilly portion of a city. An important consideration is how sleep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100kg, can accelerate on a level road from rest to 21m/s
Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig 4-58). She notices that the string make angle of 25o with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18s.
A 28.0-kg block is connected to an empty 1.35-kg bucket by a cord running over a frictionless pulley (Fig. Fig 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320. Sand is gradually added
In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the
(a) What minimum force F is needed to lift the piano (mass M) using the pulley apparatus shown in Fig. 4-60?(b) Determine the tension in each section of rope: FT1, FT2, FT3 and FT4.
A jet aircraft is accelerating at 3.5 m/s2 at an angle of 45o above the horizontal. What is the total force the cockpit seat exerts on the 75-kg pilot?
In the design process for a child-restraint chair an engineer considers the following set of conditions: A 12-kg child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-61). Assume the auto-mobile is involved in a head-on collision with another vehicle. The
A 7590-kg helicopter accelerates upward at 0.80 m/s2 while lifting a 1250-kg frame at a construction site, Fig. 4-62.(a) What is the lift force exerted by the air on the helicopter rotors?(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?(c) What force
A super high-speed 12-car Italian train has a mass of 660 metric tons (660, 000kg). IT can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity (300km/h), it exerts a force of about 150 kN. Calculate(a) Its maximum acceleration, and (b) Estimate the force of
A 65-kg ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is μk = 0.10, how fast was she moving at the start of her coast?
Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen€™s rope is more elastic, called a dynamic rope by climbers Bill has a static rope, not recommended for safety purposes in pro climbing. Karen fall freely about 2.0m and then the rope stops her over a distance of
A fisherman in a boat is using a “10.lb” fishing line. This means that the line can exert a force of 45 N without breaking (1 lb = 4.45 N). (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0m/s2, what
An elevator in a tall building is allowed to reach a maximum speed of 3.5m/s going down. What must the tension be in the cable to stop this elevator over a distance of 2.6m if the elevator has a mass of 1300kg including occupants?
Two boxes, m1 = 1.0kg with a coefficient of kinetic friction of 0.10, and m2 = 2.0kg with a coefficient of 0.20, are placed on a plane inclined at 0 = 30o.(a) What acceleration does each box experience?(b) If a taut string is connected to the boxes (Fig. 4-64), with m2 initially farther down the
A 750-kg person stands on a scale in an elevator. What does the scale read (in N and in kg) when the elevator is (a) At rest,(b) Ascending at a constant speed of 3.0 m/s,(c) Falling at 3.0m/sm(d) Accelerating upward at 3.0 m/s2,(e) Accelerating downward at 3.0 m/s2?
Three mountain climbers who are roped together are ascending an ice field inclined at 21.0o to the horizontal. The lat climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75kg, calculate the tension in each of the two
Sometimes people say that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement?
Will the acceleration of a car be the same when the car travels around a sharp curve at a constant 60km/h as when it travels around a gentle curve at the same speed? Explain
Suppose a car moves at constant speed along a hilly road, where does the car exert the greatest and least forces on the road:(a) At the top of a hill,(b) At a dip between two hills,(c) On a level stretch near the bottom of a hill?
Describe all the forces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the child?
A bucket of water can be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.
How many “accelerators” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?
Calculate the force of Earth’s gravity on a spacecraft 12.800km (2 Earth radii) above the Earth’s surface it its mass is 1350kg.
A child on a sled come flying over the crest of a small hill, as shown in Fig. 5-31. His sled does not leave the ground (he does not achieve €œair€), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using
At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.00m/s2. A 21.0-kg brass ball is transported to this planet. What is (a) The mass of the brass ball on the Earth and on the planet, and (b) The weight of the brass ball on the Earth and on the planet?
Calculate the acceleration due to gravity on the Moon. The Moon’s radius is 1.74 x 106 m and its mass is 7.35 x 1022 kg.
Why do bicycle riders lean inward when rounding a curve at high speed?
A hypothetical planet has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?
Why do airplanes bank when they turn?? How would you compute the banking angle given its speed and radius of the turn?
A hypothetical planet has a mass 1.66 time that of Earth, but the same radius. What is g near its surface?
A girl is whirling a ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?
Two objects attract each other gravitationally with a force of 2.5 x 10-10 N when they are 0.25 m apart. Their total mass is 4.0 kg. Find their individual masses.
Calculate the effective valued of g, the acceleration of gravity at (a) 3200m, and (b) 3200km, above the Earth’s surface
A child sitting 1.10m from the center of a merry-go-round moves with a speed of 1.25m/s. Calculate (a) The centripetal acceleration of the child, and (b) The net horizontal force exerted on the child (mass = 25.0kg)
What is the distance from the Earth’s center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/10 of its value at the Earth’s surface?
A jet plane travelling 1890 km/h (525m/s) pulls out of a dive by moving in an are of radius 6.00km. What is the plane’s acceleration if g’s?
A certain neutron star has five times the mass of our Sun packet into a sphere about 10 km in radius. Estimate the surface gravity on this monster.
Calculate the centripetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth’s orbit is a circle of radius 1.50 x 1011 m.
A typical white-dwarf star, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun what is the surface gravity on this star?
A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90m. Calculate the speed of the discus.
You are explaining why astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t sp by calculating the acceleration of gravity 250km above the Earth’s surface in terms
Four 9.5-kg spheres are located at the corners of a square of side 0.60m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three.
Suppose the space shuttle is in orbit 400km from the Earth’s surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth’s surface.
What is the magnitude of the acceleration of a speck of clay on the edge of potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32cm?
Every few hundred years most of the up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are MV = 0.815 ME, 318ME, MS = 95.1 ME, and their mean distances from the Sun are 108, 150,
Given that acceleration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400km, determine the mass of Mars.
A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm, as shown in Fig. 5-33. If its speed is 4.00 m/s and its mass is 0.300kg, calculate the tension in the string when the ball is(a) At the top of its path, and(b) At the bottom of its path.
A 0.45-kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75N, what is the maximum speed the ball can have?
Determine the mass of the Sun using the known value for the period of the Earth and its distance from the Sun.
What is the maximum speed with which a 1050-kg car can round a turn of radius 77m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?
Calculate the speed of a satellite movie in a stable circular orbit about the Earth at a height of 3600 km.
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 85m at a speed of 95km/h?
The space shuttle releases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?
A device for training astronauts and jet fighter pilots is designed to rotate a trainee is horizontal circle of radius 12.0m. If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? Express your answer in both m/s and rev/s.

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