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physics
mechanics
Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions
A 975-kg sports car accelerates from rest to 95km/h in 6.4 s. What is the average power delivered by the engine?
During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33° angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance.
A pump lifts 27.0 kg of water per minute through a height of 3.50 m. What minimum output rating (watts) must the pump motor have?
A ski area claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.
In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to
What minimum horsepower must a motor have to be able to drag a 370-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 6.0° hill at a steady speed of 4.0 m/s. Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?
Spiderman uses his spider webs to save a runaway train moving about 60km/h Fig. 6-44. His web stretches a few city blocks (500 m) before the 104 -kg train comes to a stop. Assuming the web acts like a spring, estimate the effective spring constant.
A 36.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?
An elevator cable breaks when a 925-kg elevator is 28.5 m above the top of a huge spring (k = 8.00 × 104 N/m) at the bottom of the shaft. Calculate(a) The work done by gravity on the elevator before it hits the spring;(b) The speed of the elevator just before striking the spring;(c) The amount the
(a) A 3.0-g locust reaches a speed of 3.0 m/s during its jump. What is its kinetic energy at this speed? (b) If the locust transforms energy with 35% efficiency, how much energy is required for the jump?
In a common test for cardiac function (the "stress test"), the patient walks on an inclined treadmill (Fig. 6-46). Estimate the power required from a 75-kg patient when the treadmill is sloping at an angle of 12° and the velocity is 3.1 km/h (How does this power compare to the power rating of a
An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snow bank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot's mass was 88 kg and his speed at impact was 45 m/s, estimate: (a) The work done by the snow
Many cars have "bumpers" that are designed to compress and rebound elastically without any physical damage at speeds below If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must be the effective spring
In climbing up a rope, a 62-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this feat?
If a 1300-kg car can accelerate from 35km/h to 65km/h in 3.8 s, how long will it take to accelerate from 55km/h to 95km/h? Assume the power stays the same, and neglect frictional losses.
A cyclist starts from rest and coasts down a 4.0° hill. The mass of the cyclist plus bicycle is 85 kg. After the cyclist has traveled 180 m,(a) What was the net work done by gravity on the cyclist?(b) How fast is the cyclist going? Ignore air resistance and friction.
Water flows over a dam at the rate of 680 kg/s and falls vertically 88 m before striking the turbine blades. Calculate(a) The speed of the water just before striking the turbine blades (neglect air resistance),(b) The rate at which mechanical energy is transferred to the turbine blades, assuming
A 65-kg hiker climbs to the top of a mountain 4200 m high. The climb is made in 4.6 h starting at an elevation of 2800 m. Calculate (a) The work done by the hiker against gravity, (b) The average power output in watts and in horsepower, (c) Assuming the body is 15% efficient, what rate of energy
A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of 2.0 m/s for 7.0 s. Find the net work done on the box.
An 18-kg sled starts up a 28° incline with a speed of 2.3m/s. The coefficient of kinetic friction is µk = 0.25.(a) How far up the incline does the sled travel?(b) What condition must you put on the coefficient of static friction if the sled is not to get stuck at the point determined in part
Some electric power companies use water to store energy. Water is pumped from a low reservoir to a high reservoir. To store the energy produced in 1.0 hour by a 180-MW electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper
A softball having a mass of 0.25 kg is pitched horizontally at 120 km/h. 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. The distance between the plate and the pitcher is about 15 m.
The brakes on a truck can overheat and catch on fire if the truck goes down a long steep hill without shifting into a lower gear. (a) Explain why this happens in terms of energy and power. (b) Would it matter if the same elevation change was made going down a steep hill or a gradual hill? Explain
(a) Only two conservative forces are discussed in this Chapter. What are they, and how are they accounted for when you are dealing with conservation of energy? (b) Not mentioned is the force of water on a swimmer. Is it conservative or nonconservative?
The speed of a tennis ball on the return of a serve can be just as fast as the serve, even though the racket isn't swung very fast. How can this be?
If a 20-passenger plane is not full, sometimes passengers are told they must sit in certain seats and may not move to empty seats. Why might this be?
Bob and Jim decide to play tug-of-war on a frictionless (icy) surface. Jim is considerably stronger than Bob, but Bob weighs 160 lb whereas Jim weighs 145 lb. Who loses by crossing over the midline first? Explain.
In one type of nuclear radioactive decay, an electron and a recoil nucleus are emitted but often do not separate along the same line. Use conservation of momentum in two dimensions to explain why this implies the emission of at least one other particle (it came to be called a "neutrino").
1. A truck going 15 km/h has a head-on collision with a small car going 30 km/h. Which statement best describes the situation? (a) The truck has the greater change of momentum because it has the greater mass. (b) The car has the greater change of momentum because it has the greater speed. (c)
1. Two identical billiard balls traveling at the same speed have a head-on collision and rebound. If the balls had twice the mass, but maintained the same size and speed, how would the rebound be different? (a) At a higher speed. (b) At slower speed. (c) No difference. 2. An astronaut is a short
1. A space vehicle, in circular orbit around the Earth, collides with a small asteroid which ends up in the vehicle's storage bay. For this collision, (a) Only momentum is conserved. (b) Only kinetic energy is conserved. (c) Both momentum and kinetic energy are conserved. (d) Neither momentum nor
1. You are lying in bed and want to shut your bedroom door. You have a bouncy ball and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it? (a) The super ball. (b) The blob of clay. (c) Both the same. (d) Neither will work. 2. A baseball is
1. A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push first the car and then the truck for the same amount of time with the same force, what can you say about the momentum and kinetic energy (KE) of the car and the truck? Ignore
A 22-g bullet traveling 240 m/s penetrates a 2.0-kg block of wood and emerges going 150m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?
A 0.145-kg baseball pitched horizontally at 27.0 m/s strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact.
Air in a 120-km/h wind strikes head-on the face of a building 45 m wide by 75 m high and is brought to rest. If air has a mass of 1.3 kg per cubic meter, determine the average force of the wind on the building.
A 725-kg two-stage rocket is traveling at a speed of 6.60 × 103 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.08 × 103 m/s relative to each other along the original line of motion.(a) What is the speed and
A 0.145-kg baseball pitched at 31.0 m/s is hit on a horizontal line drive straight back at 46.0 m/s. the pitcher at If the contact time between bat and ball 5.00 × 10-3 s, is calculate the force (assumed to be constant) between the ball and bat.
A golf ball of mass 0.045 kg is hit off the tee at a speed of 38 m/s. The golf club was in contact with the ball for Find 3.5 × 10-3 s. (a) The impulse imparted to the golf ball. (b) The average force exerted on the ball by the golf club.
A 12-kg hammer strikes a nail at a velocity of 7.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (b) What is the average force acting on the nail?
A tennis ball of mass m = 0.060 kg and speed v = 28m/s strikes a wall at a 45° angle and rebounds with the same speed at 45° (Fig. 7-32). What is the impulse (magnitude and direction) given to the ball?
A 125-kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with her legs from a 1900-kg space capsule.(a) What is the change in speed of the space capsule?(b) If the push lasts 0.600 s, what is the average force exerted by each on the other? As the reference frame, use
A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow. What is the skier's change in velocity?
Rain is falling at the rate of 2.5 cm/h and accumulates in a pan. If the raindrops hit at 8.0 m/s, estimate the force on the bottom of a 1.0-m2 pan due to the impacting rain which we assume does not rebound. Water has a mass of 1.00 × 103 kg per m3.
A 95-kg fullback is running at 3.0 m/s to the east and is stopped in 0.85 s by a head-on tackle by a tackler running due west. Calculate (a) The original momentum of the fullback, (b) The impulse exerted on the fullback, (c) The impulse exerted on the tackler, (d) The average force exerted on
With what impulse does a 0.50-kg newspaper have to be thrown to give it a velocity of 3.0 m/s?
(a) Calculate the impulse experienced when a 55-kg person lands on firm ground after jumping from a height of 2.8 m.(b) Estimate the average force exerted on the person's feet by the ground if the landing is stiff-legged, and again(c) With bent legs. With stiff legs, assume the body moves 1.0 cm
A ball of mass 0.440 kg moving east (+ x direction) with a speed of 3.80 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?
A 0.450-kg hockey puck, moving east with a speed of 5.80 m/s, has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each puck after the collision?
A 0.060-kg tennis ball, moving with a speed of has a head-on collision with a 0.090-kg ball initially moving in the same direction at a speed of Assuming a perfectly elastic collision, determine the speed and direction of each ball after the collision.
Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball's initial speed was 2.00 m/s, and the other's was 3.60 m/s in the opposite direction, what will be their speeds and directions after the collision?
A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball?
A ball of mass 0.220 kg that is moving with a speed of 5.5 m/s collides head-on and elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a speed of 3.8 m/s.Calculate(a) The velocity of the target ball after the collision,(b) The
Determine the fraction of kinetic energy lost by a neutron (m1 = 1.01 u) when it collides head-on and elastically with a target particle at rest which is (a) 11H (m = 1.01u); (b) 21H (heavy hydrogen, m = 2.01 u); (c) 126C (m = 12.00 u); (d) 20882Pb (lead, m = 208 u).
(a) Derive a formula for the fraction of kinetic energy lost, ∆KE/KE, in terms of m and M for the ballistic pendulum collision of Example 7-9.(b) Evaluate for m = 18.0g and M = 380 g.
A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's maximum displacement
An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 5500 J is released in the explosion, how much kinetic energy does each piece acquire?
A 980-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the
You drop a 14-g ball from a height of 1.5 m and it only bounces back to a height of 0.85 m. What was the total impulse on the ball when it hit the floor? (Ignore air resistance.)
A 110-kg tackler moving at 2.5 m/s meets head-on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after the collision?
A 144-g baseball moving 28.0 m/s strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at 1.10m/s. (a) What is the baseball's speed after the collision? (b) Find
Billiard ball A of mass mA = 0.120kg moving with speed vA = 2.80m/s strikes ball B, initially at rest, of mass mB = 0.140 kg. As a result of the collision, ball A is deflected off at an angle of 30.0° with a speed v'A = 2.10 m/s.(a) Taking the x axis to be the original direction of motion of ball
A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of 9.6 × 10-23 kg · m/s and 6.2 × 10-23 kg · m/s, respectively. Determine the magnitude and the direction of the momentum of the second
Billiard balls A and B, of equal mass, move at right angles and meet at the origin of an xy coordinate system as shown in Fig. 7-36. Initially ball A is moving along the y axis at + 2.0 m/s, and ball B is moving to the right along the x axis with speed + 3.7m/s. After the collision (assumed
An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°.(a) At what angle does the target particle move after the collision?(b) What are the final speeds of the two particles?(c) What fraction of the
Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of 1300 kg/s with a speed of 4.5 × 104 m/s.
The CM of an empty 1250-kg car is 2.40 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 65.0 kg.
Determine the CM of the uniform thin L-shaped construction brace shown in Fig. 7-40.
A 7700-kg boxcar traveling 14 m/s strikes a second car at rest. The two stick together and move off with a speed of 5.0 m/s. What is the mass of the second car?
Suppose that in Example 7-14 (Fig. 7-28),(a) Where then would land?(b) What if
Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 58 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.0 m apart from each other, now exchange seats. How far and in what direction will the boat move?
Two astronauts, one of mass 55 kg and the other 85 kg, are initially at rest together in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?
Two asteroids strike head-on: before the collision, asteroid A (mA = 7.5 × 1012 kg) has velocity 3.3 km/s and asteroid B (mA = 7.5 × 1012 kg) has velocity 1.4 km/s in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after
A ball is dropped from a height of 1.60 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?
A child in a boat throws a 5.30-kg package out horizontally with a speed of 10.0 m/s, Fig. 7-31. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and the mass of the boat is 35.0 kg.
A 4800-kg open railroad car coasts at a constant speed of 7.60 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.80kg/min. Ignoring friction with the tracks, what is the car's speed after 60.0 min?
Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7-43). Car A has a mass of 435 kg and car B 495 kg, owing to differences in passenger mass. If car A approaches at 4.50m/s and car B is moving at 3.70 m/s, calculate(a) Their
A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 7-44. If the bullet has a mass of 25.0 g and a speed of 230 m/s, how high will the block rise into the air after the bullet becomes embedded in it?
You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1500 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he skidded and crashed into car B. After the collision, car
A meteor whose mass was about 1.5 × 108 kg struck the Earth (mE = 6.0 × 1024 kg) with a speed of about 25 km/s and came to rest in the Earth.(a) What was the Earth's recoil speed (relative to Earth at rest before the collision)?(b) What fraction of the meteor's kinetic energy was transformed to
A 28-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the
You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 45 km/h. A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on
Two balls, of masses mA = 45g and mB = 65g, are suspended as shown in Fig. 7-46. The lighter ball is pulled away to a 66° angle with the vertical and released.(a) What is the velocity of the lighter ball before impact?(b) What is the velocity of each ball after the elastic collision?(c) What
An atomic nucleus at rest decays radioactively into an alpha particle and a different nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is 2.8 × 105 m/s? Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.
The space shuttle launches an 850-kg satellite by ejecting it from the cargo bay. The ejection mechanism is activated and is in contact with the satellite for 4.8 s to give it a velocity of 0.30 m\s in the x direction relative to the shuttle. The mass of the shuttle is 92,000 kg.(a) Determine the
Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at 15km/s. How much destructive
An astronaut of mass 210 kg including his suit and jet pack wants to acquire a velocity of to move back toward his space shuttle. Assuming the jet pack can eject gas with a velocity of 2.0 m/s, what mass of gas will need to be ejected?
Two blocks of mass mA and mB, resting on a frictionless table, are connected by a stretched spring and then released (Fig. 7-48).(a) Is there a net external force on the system before release?(b) Determine the ratio of their speeds, vA/vB.(c) What is the ratio of their kinetic energies?(d) Describe
A mass less spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then
An atomic nucleus initially moving at320 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 280 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?
Consider the Examples in this Chapter involving ΣF(vector)ext = Δp(vector)/Δt. Provide some general guidelines as to when it is best to solve the problem using ΣF(vector)ext = 0 so Σp(vector)i = Σp(vector)f, and when to use the principle of impulse instead so that ΣF(vector)ext Δt =
A 6.0-kg object moving in the + x direction at 6.5 m/s collides head-on with an 8.0-kg object moving in the - x direction at 4.0 m/s. Determine the final velocity of each object if:(a) The objects stick together;(b) The collision is elastic;(c) The 6.0-kg object is at rest after the collision;(d)
A bicycle odometer (which counts revolutions and is calibrated to report distance traveled) is attached near the wheel axle and is calibrated for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?
When a motorcyclist leaves the ground on a jump and leaves the throttle on (so the rear wheel spins), why does the front of the cycle rise up?
The book has three symmetry axes through its center, all mutually perpendicular. The book's moment of inertia would be smallest about which of the three? Explain.
Can the mass of a rigid object be considered concentrated at its CM for rotational motion? Explain.
1. A car speedometer that is supposed to read the linear speed of the car uses a device that actually measures the angular speed of the tires. If larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading?The speedometer(a) Will still read the speed
1. Two wheels having the same radius and mass rotate at the same angular velocity (Fig. 8-38). One wheel is made with spokes so nearly all the mass is at the rim. The other is a solid disk. How do their rotational kinetic energies compare? (a) They are nearly the same. (b) The wheel with spokes has
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