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physics
mechanics

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

At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60? Assume the spaceship’s diameter is 32m, and give your answer as the time needed for one revolution (See question 21, Fig 5-32.)
A coin is placed 11.0cm 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 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and
Determine the time it takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does you result depend on the mass of the satellite?
At what minimum speed musty a roller coaster be traveling when upside down at the top of a circle (Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4m.
At what horizontal velocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?
A sports car of mass 950 kg (including the driver) crosses the rounded top of a hill (radius = 95m) at 22m/s Determine (a) The normal force exerted by the road on the car, (b) The normal force exerted by the car on the 72-kg driver, and (c) The car speed at which the normal force on the driver
During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 100km. How long did it take to go around the Moon once?
How many revolutions per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?
A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10m. 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 bucket.(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?
How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000 g’s?
In a €œRotor-ride€ at a camival, people are rotated in a cylindrically walled €œroom€. (See Fig. 5-35). The room radius is 4.6m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static
A flat puck (mass M) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass M) through a central hole as shown in Fig. 5-36. Show that the speed of the puck is given by
Redo Example 5-3, precisely this time, by not ignoring the weight of the ball which revolves on a string 0.600m long. In particular, find the magnitude of FT, and the angle it makes with the horizontal.
If a curve with a radius of 88m is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95 km/h?
A 1200-kg car rounds a curve of radius 67m banked at an angle of 12o. If the car is traveling at 95km/g, will a friction force be required If so, how much and in what direction?
Two blocks, of masses m1 and m2, are connected to each other and to a central post by cords as shown in Fig, 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances r1 and r2 from the post. Derive and algebraic expression for the
A pilot performs an evasive maneuver by diving vertically at 310m/s. If he can withstand an acceleration of 9.0g’s without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?
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 15m/s. The car’s mass is 1100kg.
A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 320 km/h in a semicircular are with a radius of 22m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve
A particle revolves in a horizontal circle of radius 2.90m. At a particular instant, its acceleration is 1.05m/s2, in a direction that makes and angle of 32.0o to its direction of motion. Determine its speed (a) At this moment and (b) 2.00s later, assuming constant tangential acceleration.
How much work is done by the gravitational force when a 264-kg pile driver falls 2.80m?
A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is required?
A 1300-N crate rests on the floor. How much work is required to move it at constant speed(a) 4.0 m along the floor against a friction force of 230N, and (a) 4.0 m vertically?
How much work did the movers do (horizontally) pushing a 160-kg crate 10.3 across a rough floor without acceleration, if the effective coefficient of friction was 0.50?
A box of mass 5.0 kg if accelerated from rest across a floor at a rate of 2.0 m/s2 fro 7.0s find the net work done on the box.
Eight books, each 4.3 cm thick with mass 1.7 kg, lie flat on a table. How much work is required to stack them one on top of another?
A lever such as that shown in Fig. 6-35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, Fo, to input force, F1, is related to the lengths, l1and lo from the pivot point by Fo/F1 = l1/lo (ignoring friction and the mass of the lever), given
A 330-kg piano slide 3.6m down a 28o incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). The effective coefficient of kinetic friction is 0.40. Calculate:(a) The force exerted by the man,(b) The work done by the man on the piano,(c) The work
(a) Fine the force required to give a helicopter of mss M an acceleration of 0.10 g upward. (b) Find the work done by this force ad the helicopter moves a distance h upward.
What is the minimum work needed to push a 950-kg car 810m up along a 9.0 incline?(a) Ignore friction.(b) Assume the effective coefficient of friction retarding the car is 0.25.
In Fig. 6-6a, assume the distance axis is linear and that dA = 10.0m and dB = 35.0m. Estimate the work done by force F in moving a 2.80-kg object from dA to dA.
The force on an object, acting along the x axis, varies as shown in Fig. 6-37. Determine the work done by this force to move the object(a) From x = 0.0 to x = 10.00m, and(b) From x = 0.0 to x = 15.0m.
A spring has k = 88 N/m. Use a graph to determine the work needed to stretch it from x = 3.8cm to x = 5.8cm, where x is the displacement from its unstretched length.
The net force exerted on a particle acts in the + x direction. Its magnitude increases linearly from zero at x = 0, to 24.0 N at x = 3.0m. It remains constant at 24.0 N from x = 3.0m to x =8.0m, and then decreases linearly to zero at x = 0 to x = 13.0m graphically by determining the area under the
At room temperature, an oxygen molecule, with mass of 5.31 x 10-26 kg, typically has a KE of about 6.21 x 10-21 J. How fast is the molecule moving?
(a) If the KE of an arrow is doubled, by what factor has its speed increased? (b) If its speed is doubles, by what factor does its KE increase?
How much work is required to stop an electron (m = 9.11 x 10-31 kg) which is moving with a speed of 1.90 x 106 m/s?
How much work must be done to stop a 1250-kg car traveling at 105 km/h?
An 88-g arrow is fired from a bow whose string exerts an average force of 110N on the arrow over a distance of 78cm. What is the speed of the arrow as it leaves the bow?
A baseball (m = 140g) traveling 32m/s moves a fielder’s glove backward 25cm when the ball is caught. What was the average force exerted by the ball on the glove?
If the speed of a car is increased by 50% by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver’s reaction time.
At an accident scene on a level road, investigators measure a car’s skid mark to be 88m long. The accident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the
A softball having a mass of 0.25kg is pitched at 95km/g. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is about 15m.
How high will a 1.85-kg rock go it thrown straight up by someone who does 80.0J of work on it? Neglect air resistance.
A 285-kg load is lifted 22.0m 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 cable on the load, (d) The work done by gravity on the load, and (e) The final speed of the load assuming
A spring has a spring stiffness constant, k, of 440 N/m. How much must this spring be stretched to store 25J of potential energy?
A 7.0-kg monkey swings from one branch to another 1.2 higher. What is the change in potential energy?
By how much does the gravitational potential energy of a 64-kg pole vaulted change if his center of mass rises about 4.0m during the jump?
A 1200-kg car rolling on a horizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2m. What is the spring stiffness constant of the spring?
A 1.60-m tell person lifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to? (a) The ground, and (b) The top of the person’s head?(c) How is the work done by the person related to the answers in parts (a) and (b)?
A 55-kg hiker starts at an elevation of 1600m and climbs to the top of a 3300-m peak.(a) What is the hiker’s change in potential energy?(b) What is the minimum work required of the hiker?(c) Can the actual work done be more than this? Explain why.
A spring with k = 53N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?
Jane, looking of Tarzan, is running at top speed (5.3m/s) 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 answer?
A novice skier, starting from rest, slides down a frictionless 35.0o incline whose vertical height is 185 m. how fast is she going when she reaches the bottom?
A sled is initially given a shove up a frictionless 28.0o incline. It reaches a maximum vertical height 1.35m higher than where it started. What was its initial speed?
In the high jump, Fran’s kinetic energy is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass 2.10m and cross the bar with a speed of 0.70 m/s?
A 65-kg trampoline artist jumps vertically upward from the top of a platform with speed of 5.0 m/s.(a) How fast is he going as he lands on the trampoline, 3.0m below (Fig. 6-38)?(b) If the trampoline behaves like a spring with spring stiffness constant 6.2 x 104 N/m, how far does he depress it?
A projectile is fired at an upward angle of 45.0o from the top of a 265-m cliff with a speed of 185m/s. What will be its speed when it strikes the ground below? (Use conservation of energy.)
A vertical spring (ignore its mass). Whose spring stiffness constant is 950 N/m.(a) What upward speed can it give to a 0.30-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?
A block of mass m slides without friction along the looped track shown in Fig. 6-39. If the block is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height h must it be released?
A block of mass m is attached to the end of a spring (spring stiffness constant k). Fig. 6-40. The block is given an initial displacement xo, after which is oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of xo,
A 62-kg bungee jumper jumps from a bride, she is tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31m.(a) Calculate the spring stiffness constant k of the bungee cord, assuming. Hooke’s law applies.(b) Calculate the maximum acceleration she experiences.
The roller-coaster car shown in Fig. 6-41 is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4.
A 0.40-kg ball is thrown with a speed of 12 m/s at an angle of 33o.(a) What is its speed at its highest point, and (b) How high does it go? (Use conservation of energy, and ignore air resistance.)
An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo and acceleration of
A cyclist intends to cycle up a 7.8o hill whose vertical height is 150m. Assuming the mass of bicycle plus cyclist is 75kg, (a) Calculate how much work must be done against gravity. (b) If each complete revolution of the pedals moves the bike 5.1m along its path, calculate the average force that
Two railroad cars, each of mass 7650kg and traveling 95km/h in opposite directions, collide head-on and com to rest. How much thermal energy is produced in this collision?
A 21.7-kg child descends a slide 3.5m high and reaches the bottom with a speed of 2.2m/s. How much thermal energy due to friction was generated in this process?
A ski starts from rest and slides down a 22o incline 75 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 the incline and has the same coefficient of friction, how far will the ski travel along the
A 145-g baseball is dropped from a tree 13.0 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 8.00m/s, what is the average force of air resistance exerted on it?
You drop a ball from a height of 2.0m, and it bounces back to a height of 1.5m.(a) What fraction of its initial energy is lost during the bounce?(b) What is the ball’s speed just as it leaves the ground after the bounce? (c) Where did the energy go?
A 110-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350N. For the first 15m the floor is frictionless, and for the next 15m the coefficient of friction is 0.30. What is the final speed of the crate?
Suppose the roller coaster in Fig. 6—41 passes point 1 with a speed of 1.70 m/s. if the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0m.
A skier traveling 12.0 m/s reaches the foot of a steady upward 18.0o incline and glides 12.2 up along this slope before coming to rest. What was the average coefficient of friction?
A 0.620-kg wood block is firmly attached to a very light horizontal spring (k = 180N/m) as shown in Fig. 6-40. It is noted that the block-spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the
A 280-g wood block is firmly attached to a very light horizontal spring. Fig 6-40. The block can slide along a table where the coefficient of friction is 0.30.. Af force of 22N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it
Early test flights for the space shuttle used “glider” (mass of 980kg including pilot) that was launched horizontally at 500km/h from a height of 3500m. The glider eventually landed at a speed of 200km/h.(a) What would its landing speed have been in the absence of air resistance?(b) What was
How long will it take a 1750-W motor to lift a 315-kg piano to a sixth-story window 16.0m above?
If a car generates 18hp when traveling at a steady 88km/g, what must be the average force exerted on the car due to friction and air resistance?
A 1400-kg sports car accelerates from rest to 95 km/h in 7.4s. What is the average power delivered by the engine?
(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 lightbulb?
Electric energy units are often expressed in the form of “kilowatt-hours”. (a) Show that one kilowatt-hour (kWh) is equal to 3.6 x 10oJ.(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month, and (c) How many
A driver notices that her 1150-kg car slows down from 85 km/h to 65 km/h in about 6.0s on the level when it is in neutral. Approximately what power (watts and hp) is needed top keep the car traveling at a constant 75 km/h?
How much work can a 3.0-hp motor do in 1.0h?
A shot-putter accelerates a 73-kg shot from rest to 14m/s. If this motion takes 1.5s, what average power was developed?
A pump is to lift 18.0kg of water per minute through a height of 3.60 m. What output rating (watts) should the pump motor have?
During a workout, the football players at State U, ran up the stadium stairs in 66s. The stairs are 140 m long and inclined at an angle of 32o. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.
How fast must a cyclist climb a 6.0o hill to maintain a power output of 0.25 hp? Neglect work done by friction, and assume the mass of cyclist plus bicycle is 68kg.
A 1200-kg car has a maximum power output of 120hp. How steep a hill can it climb at a constant speed of 75km/h if the frictional forces add up to 650 N?
What minimum horsepower must a motor have to be able to drag a 310-kg box along a level floor at a speed of 1.20m/s if the coefficient of friction is 0.45?
A bicyclist coasts down a 7.0o hill at a steady speed of 5.0m/s. Assuming a total mass of 75kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?
Designers of today’s cars have built “5mi/h (8km/h) bumpers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h. IF the material of the bumpers permanently deforms after a compression of 1.5cm, but remains like an elastic spring up to that
In a certain library the first shelf is 10.0cm off the ground, and the remaining four shelves are each spaced 30.0cm above the previous one. If the average book has a mass of 1.5 kg with a height of cm, and an average shelf holds 25 books, how much work is required to fill all the shelves, assuming
The rings of Saturn are composed of chunks of ice that or bit the planet. The inner radius of the rings is 73,000km, while the outer radius is 170,000 km. Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with
A film of Jesse Owens€™s famous long jump (Fig.6-42) in the 1936 Olympics shows that his center of mass rose 1.1m from launch point to the top of the are What minimum speed did he need at launch if he was traveling at 6.5 m/s at the top of the are?
A Ferris wheel 24.0m in diameter rotates once every 15.5s (see Fig. 5-9). What is the ratio of a person’s apparent weight to her real weight?(a) At the top, and (b) At the bottom?
What is the apparent weight of a 75-kg astronaut 4200km from the center of the Earth’s Moon in a space vehicle?(a) Moving at constant velocity, and (b) Accelerating toward the Moon at 2.9m/s2? State the “direction” in each case.
The block of mass m sliding without friction along the looped track shown in Fig. 6-39 is to remain on the track at all times, even at the very top of the loop of radius r.(a) In terms of the given quantities, determine the minimum release height h (as in Problem 40). Next, if the actual release
Suppose that a binary-star system consists of two stars of equal mass. They are observed to the separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?
What will a spring scale read for the weight of a 55-kg woman in an elevator that moves (a) Upward with constant speed of 6.0m/s.(b) Downward with constant speed of 6.0m/s(c) Upward with acceleration of 0.33g,(d) Downward with acceleration 0.33 g, and (e) In free fall?

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