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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

Can centripetal acceleration change the speed of circular motion? Explain.
(a) Find the acceleration due to Earth’s gravity at the distance of the Moon.(b) Calculate the centripetal acceleration needed to keep the Moon in its orbit (assuming a circular orbit about a fixed Earth), and compare it with the value of the acceleration due to Earth’s gravity that you have
In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is a fictitious force sensed and
Helicopter blades withstand tremendous stresses. In addition to supporting the weight of a helicopter, they are spun at rapid rates and experience large centripetal accelerations, especially at the tip.(a) Calculate the magnitude of the centripetal acceleration at the tip of a 4.00 m long
Riders in an amusement park ride shaped like a Viking ship hung from a large pivot are rotated back and forth like a rigid pendulum. Sometime near the middle of the ride, the ship is momentarily motionless at the top of its circular arc. The ship then swings down under the influence of gravity. The
Critical Thinking A car travels around a loop with negligible friction at a constant speed and never loses contact with the loop. The top of the loop is labeled A and the bottom of the loop is labeled B.(a) At what point would the normal force be greatest? Briefly explain your reasoning.(b) Based
A Saturn V's mass at liftoff was 2.80 × 106 kg, its fuel-burn rate was 1.40 × 104 kg/s, and the exhaust velocity was 2.40 x 103 m/s. Calculate its initial acceleration.StrategyThis problem is a straightforward application of the expression for acceleration because is the unknown and all of the
If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter.
Under what circumstances is momentum conserved?
Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?
A professional boxer hits his opponent with a 1000-N horizontal blow that lasts for 0.150 s.(a) Calculate the impulse imparted by this blow. (b) What is the opponent’s final velocity, if his mass is 105 kg and he is motionless in midair when struck near his center of mass? (c) Calculate the
Momentum for a system can be conserved in one direction while not being conserved in another. What is the angle between the directions? Give an example.
Suppose a child drives a bumper car head on into the side rail, which exerts a force of 4000 N on the car for 0.200 s.(a) What impulse is imparted by this force?(b) Find the final velocity of the bumper car if its initial velocity was 2.80 m/s and the car plus driver have a mass of 200 kg. You may
Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.
One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100-mg chip of paint
Can objects in a system have momentum while the momentum of the system is zero? Explain your answer.
A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment.(a) Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm.(b) Calculate the average force on the person if he is stopped by an air bag
Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.
Military rifles have a mechanism for reducing the recoil forces of the gun on the person firing it. An internal part recoils over a relatively large distance and is stopped by damping mechanisms in the gun. The larger distance reduces the average force needed to stop the internal part.(a) Calculate
What is an elastic collision?
What is an inelastic collision? What is a perfectly inelastic collision?
Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s but collides head-on with a padded goalpost and experiences a backward force of 1.76 × 104 N for 5.50 × 10-2 s.
Mixed-pair ice skaters performing in a show are standing motionless at arms length just before starting a routine. They reach out, clasp hands, and pull themselves together by only using their arms. Assuming there is no friction between the blades of their skates and the ice, what is their velocity
Water from a fire hose is directed horizontally against a wall at a rate of 50.0 kg/s and a speed of 42.0 m/s. Calculate the magnitude of the force exerted on the wall, assuming the water’s horizontal momentum is reduced to zero.
A small pickup truck that has a camper shell slowly coasts toward a red light with negligible friction. Two dogs in the back of the truck are moving and making various inelastic collisions with each other and the walls. What is the effect of the dogs on the motion of the center of mass of the
Figure 8.14 shows a cube at rest and a small object heading toward it.(a) Describe the directions (angle θ1 ) at which the small object can emerge after colliding elastically with the cube. How does θ1 depend on b, the so-called impact parameter? Ignore any effects that might be due to rotation
A 0.450-kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. (a) Calculate the duration of the impact. (b) What was the average force exerted on the nail?
Starting with the definitions of momentum and kinetic energy, derive an equation for the kinetic energy of a particle expressed as a function of its momentum.
Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. How is the motion of the center of mass affected by the explosion? How would it be affected if the pieces experienced significantly more air resistance than the intact shell?
A ball with an initial velocity of 10 m/s moves at an angle 60° above the +x-direction. The ball hits a vertical wall and bounces off so that it is moving 60° above the -x-direction with the same speed. In terms of m, the mass of the ball, what is the impulse delivered by the wall?
During a visit to the International Space Station, an astronaut was positioned motionless in the center of the station, out of reach of any solid object on which he could exert a force. Suggest a method by which he could move himself away from this position, and explain the physics involved.
A punter drops a ball from rest vertically 1 meter down onto his foot. The ball leaves the foot with a speed of 18 m/s at an angle 55° above the horizontal. In terms of m, the mass of the ball, what is the impulse delivered by the foot (magnitude and direction)?
It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and gas momentum are in the same direction as that of the rocket. How is the rocket still able to obtain thrust by ejecting the gases?
Suppose a clay model of a koala bear has a mass of 0.200 kg and slides on ice at a speed of 0.750 m/s. It runs into another clay model, which is initially motionless and has a mass of 0.350 kg. Both being soft clay, they naturally stick together. What is their final velocity?
A car moving at 10 m/s crashes into a tree and stops in 0.26 s.Calculate the force the seatbelt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg. Would the answer to this question be different if the car with the 70-kg passenger had collided with a car
What is the velocity of a 900-kg car initially moving at 30.0 m/s, just after it hits a 150-kg deer initially running at 12.0 m/s in the same direction? Assume the deer remains on the car.
A 1.80-kg falcon catches a 0.650-kg dove from behind in midair. What is their velocity after impact if the falcon’s velocity is initially 28.0 m/s and the dove’s velocity is 7.00 m/s in the same direction?
Two identical objects (such as billiard balls) have a one-dimensional collision in which one is initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. Show that both momentum and kinetic energy are conserved.
Two piloted satellites approach one another at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00 x 103 kg, and the second a mass of 7.50 x 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity?
A 70.0-kg ice hockey goalie, originally at rest, catches a 0.150-kg hockey puck slapped at him at a velocity of 35.0 m/s. Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction from which it came. What would their final velocities be in this
A 0.240-kg billiard ball that is moving at 3.00 m/s strikes the bumper of a pool table and bounces straight back at 2.40 m/s (80% of its original speed). The collision lasts 0.0150 s. (a) Calculate the average force exerted on the ball by the bumper. (b) How much kinetic energy in joules is lost
During an ice show, a 60.0-kg skater leaps into the air and is caught by an initially stationary 75.0-kg skater.(a) What is their final velocity assuming negligible friction and that the 60.0-kg skater’s original horizontal velocity is 4.00 m/s? (b) How much kinetic energy is lost?
A battleship that is 6.00 x 107 kg and is originally at rest fires a 1100-kg artillery shell horizontally with a velocity of 575 m/s. (a) If the shell is fired straight aft (toward the rear of the ship), there will be negligible friction opposing the ship's recoil. Calculate its recoil
Two piloted satellites approaching one another, at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00 x 103 kg, and the second a mass of 7.50 x 103 kg.(a) Calculate the final velocity (after docking) by using the frame of reference in which the first satellite was
A 30,000-kg freight car is coasting at 0.850 m/s with negligible friction under a hopper that dumps 110,000 kg of scrap metal into it. (a) What is the final velocity of the loaded freight car?(b) How much kinetic energy is lost?
Space probes may be separated from their launchers by exploding bolts. (They bolt away from one another.) Suppose a 4800-kg satellite uses this method to separate from the 1500-kg remains of its launcher, and that 5000 J of kinetic energy is supplied to the two parts. What are their subsequent
A 0.0250-kg bullet is accelerated from rest to a speed of 550 m/s in a 3.00-kg rifle. The pain of the rifle’s kick is much worse if you hold the gun loosely a few centimeters from your shoulder rather than holding it tightly against your shoulder.(a) Calculate the recoil velocity of the rifle if
One of the waste products of a nuclear reactor is plutonium-239 (239Pu). This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus (4He + 235U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the
The Moon's craters are remnants of meteorite collisions. Suppose a fairly large asteroid that has a mass of 5.00 x 1012 kg (about a kilometer across) strikes the Moon at a speed of 15.0 km/s.(a) At what speed does the Moon recoil after the perfectly inelastic collision (the mass of the Moon is 7.36
Two football players collide head-on in midair while trying to catch a thrown football. The first player is 95.0 kg and has an initial velocity of 6.00 m/s, while the second player is 115 kg and has an initial velocity of –3.50 m/s. What is their velocity just after impact if they cling together?
What is the speed of a garbage truck that is 1.20 x 104 kg and is initially moving at 25.0 m/s just after it hits and adheres to a trash can that is 80.0 kg and is initially at rest?
During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of 10.0 kg and the horizontal component of its velocity is 8.00 m/s when the 65.0-kg performer catches it. If the performer is on nearly frictionless roller skates, what is
Confirm that the results of the example Example 8.7 do conserve momentum in both the x- and y-directions.Data given in Example 8.7Suppose the following experiment is performed. A 0.250-kg object (m1) is slid on a frictionless surface into a dark room, where it strikes an initially stationary object
Two identical pucks collide on an air hockey table. One puck was originally at rest.(a) If the incoming puck has a speed of 6.00 m/s and scatters to an angle of 30.0° ,what is the velocity (magnitude and direction) of the second puck? (You may use the result that θ1 - θ2 = 90° for elastic
A 3000-kg cannon is mounted so that it can recoil only in the horizontal direction.(a) Calculate its recoil velocity when it fires a 15.0-kg shell at 480 m/s at an angle of 20.0° above the horizontal. (b) What is the kinetic energy of the cannon? This energy is dissipated as heat transfer in
A 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin, which is scattered at an angle of 85.0° to the initial direction of the bowling ball and with a speed of 15.0 m/s.(a) Calculate the final velocity (magnitude and direction) of the bowling ball.(b) Is the collision
Starting with equations 1 + m₂v2 cos 02 and 0= m₁v₁ sin 0₁ + m2 u2 sin 02 for conservation of momentum in the x- and y-directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses, 2 mv₁²: = 2 mu₁²+ mv'2² +mu'v'2
Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at 8.00 m/s due south. The second car has a mass of 850 kg and is approaching at 17.0 m/s due west.(a) Calculate the final velocity (magnitude and direction) of the
A 90.0-kg ice hockey player hits a 0.150-kg puck, giving the puck a velocity of 45.0 m/s. If both are initially at rest and if the ice is frictionless, how far does the player recoil in the time it takes the puck to reach the goal 15.0 m away?
Antiballistic missiles (ABMS) are designed to have very large accelerations so that they may intercept fast-moving incoming missiles in the short time available. What is the takeoff acceleration of a 10,000-kg ABM that expels 196 kg of gas per second at an exhaust velocity of 2.50 x 103 m/s?
What is the acceleration of a 5000-kg rocket taking off from the Moon, where the acceleration due to gravity is only 1.6 m/s2, if the rocket expels 8.00 kg of gas per second at an exhaust velocity of 2.20 x 103 m/s?
Calculate the increase in velocity of a 4000-kg space probe that expels 3500 kg of its mass at an exhaust velocity of 2.00 x 103 m/s. You may assume the gravitational force is negligible at the probe's location.
Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as 8.00 x 106 m/s. These techniques allow a much more favorable payload-to-fuel ratio. To illustrate this
(a) Calculate the maximum rate at which a rocket can expel gases if its acceleration cannot exceed seven times that of gravity. The mass of the rocket just as it runs out of fuel is 75,000-kg, and its exhaust velocity is 2.40 x 103 m/s. Assume that the acceleration of gravity is the same as on
Given the following data for a fire extinguisher-toy wagon rocket experiment, calculate the average exhaust velocity of the gases expelled from the extinguisher. Starting from rest, the final velocity is 10.0 m/s. The total mass is initially 75.0 kg and is 70.0 kg after the extinguisher is fired.
How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of 8.00 km/s, given that it expels gases at an exhaust velocity of 2.20 x 103 m/s?
Squids have been reported to jump from the ocean and travel 30.0 m (measured horizontally) before re-entering the water.(a) Calculate the initial speed of the squid if it leaves the water at an angle of 20.0, assuming negligible lift from the air and negligible air resistance. (b) The squid
Consider an astronaut in deep space cut free from her space ship and needing to get back to it. The astronaut has a few packages that she can throw away to move herself toward the ship. Construct a problem in which you calculate the time it takes her to get back by throwing all the packages at one
The two children shown in Figure 9.8 are balanced on a seesaw of negligible mass. (This assumption is made to keep the example simple—more involved examples will follow.) The first child has a mass of 26.0 kg and sits 1.60 m from the pivot.(a) If the second child has a mass of 32.0 kg, how far is
Consider an artillery projectile striking armor plating. Construct a problem in which you find the force exerted by the projectile on the plate. Among the things to be considered are the mass and speed of the projectile and the distance over which its speed is reduced. Your instructor may also wish
For the situation shown in Figure 9.19, calculate:(a) FR, the force exerted by the right hand, and(b) FL, the force exerted by the left hand. The hands are 0.900 m apart, and the cg of the pole is 0.600 m from the left hand.StrategyFigure 9.19 includes a free body diagram for the pole, the system
What can you say about the velocity of a moving body that is in dynamic equilibrium? Draw a sketch of such a body using clearly labeled arrows to represent all external forces on the body.
Under what conditions can a rotating body be in equilibrium? Give an example.
When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt.(a) How much torque are you exerting in newton × meters (relative to the center of the bolt)? (b) Convert this torque to footpounds.
In the wheelbarrow of Figure 9.22, the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m.(a) What upward force must you exert to support the wheelbarrow and its load if their combined mass is 45.0 kg? (b) What force does the wheelbarrow exert
Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the
What three factors affect the torque created by a force relative to a specific pivot point?
Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in Figure 9.25, and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures.StrategyThere are four forces acting on the
Use the second condition for equilibrium (net π = 0) to calculate Fp in Example 9.1, employing any data given or solved for in part (a) of the example.Data given in Example 9.1The two children shown in Figure 9.8 are balanced on a seesaw of negligible mass. (This assumption is made to keep the
A wrecking ball is being used to knock down a building. One tall unsupported concrete wall remains standing. If the wrecking ball hits the wall near the top, is the wall more likely to fall over by rotating at its base or by falling straight down? Explain your answer. How is it most likely to fall
Consider the person lifting a heavy box with his back, shown in Figure 9.28.(a) Calculate the magnitude of the force FB-in the back muscles that is needed to support the upper body plus the box and compare this with his weight. The mass of the upper body is 55.0 kg and the mass of the box is 30.0
Repeat the seesaw problem in Example 9.1 with the center of mass of the seesaw 0.160 m to the left of the pivot (on the side of the lighter child) and assuming a mass of 12.0 kg for the seesaw. The other data given in the example remain unchanged. Explicitly show how you follow the steps in the
Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this help? (It is also hazardous since it can break the bolt.)
A round pencil lying on its side as in Figure 9.12 is in neutral equilibrium relative to displacements perpendicular to its length. What is its stability relative to displacements parallel to its length?Data given in Figure 9.12 Tocw CG W NT Free-body diagram N W -Pivot point
Two children of mass 20.0 kg and 30.0 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3.00 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?
Explain the need for tall towers on a suspension bridge to ensure stable equilibrium.
(a) Calculate the magnitude and direction of the force on each foot of the horse in Figure 9.29 (two are on the ground), assuming the center of mass of the horse is midway between the feet. The total mass of the horse and rider is 500kg.(b) What is the minimum coefficient of friction between the
Suppose two children are using a uniform seesaw that is 3.00 m long and has its center of mass over the pivot. The first child has a mass of 30.0 kg and sits 1.40 m from the pivot. (a) Calculate where the second 18.0 kg child must sit to balance the seesaw.(b) What is unreasonable about the
Consider a method for measuring the mass of a person’s arm in anatomical studies. The subject lies on her back, extends her relaxed arm to the side and two scales are placed below the arm. One is placed under the elbow and the other under the back of her hand. Construct a problem in which you
You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother’s birthday. Your brother kicks a 500 g ball, which hits the top of the tree at a speed of 5 m/s and stays in contact with it for 10 ms. The ball falls to the ground near the base of the tree and the recoil of the
Suppose we replace the 4.0-kg book in Exercise 9.31 of the biceps muscle with an elastic exercise rope that obeys Hooke's Law. Assume its force constant k = 600 N/m.(a) How much is the rope stretched (past equilibrium) to provide the same force FB as in this example? Assume the rope is held in the
(a) What force should the woman in Figure 9.43 exert on the floor with each hand to do a push-up? Assume that she moves up at a constant speed.(b) The triceps muscle at the back of her upper arm has an effective lever arm of 1.75 cm, and she exerts force on the floor at a horizontal distance of
When visiting some countries, you may see a person balancing a load on the head. Explain why the center of mass of the load needs to be directly above the person’s neck vertebrae.
Scissors are like a double-lever system. Which of the simple machines in Figure 9.21 and Figure 9.22 is most analogous to scissors?Data given in Figure 9.21Data given in Figure 9.22 F Free-body diagram N 1₁ = ₁₁ 1 = ro N Fi Fn Fo Fn
A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at .500 m from the end of the plank with force F2. If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the
Suppose you pull a nail at a constant rate using a nail puller as shown in Figure 9.21. Is the nail puller in equilibrium? What if you pull the nail with some acceleration – is the nail puller in equilibrium then? In which case is the force applied to the nail puller larger and why?Data given in
A 17.0-m-high and 11.0-m-long wall under construction and its bracing are shown in Figure 9.30. The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of 650 N on each square
(a) What force must be exerted by the wind to support a 2.50-kg chicken in the position shown in Figure 9.31? (b) What is the ratio of this force to the chicken’s weight?(c) Does this support the contention that the chicken has a relatively stable construction? wind 20 cm CG W 9.0 cm
Explain the mechanical advantage of a wheelbarrow and how it explains why moving a heavy load is easier with a wheelbarrow.
Suppose the weight of the drawbridge in Figure 9.32 is supported entirely by its hinges and the opposite shore, so that its cables are slack. The mass of the bridge is 2500 kg.(a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable

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