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physics scientists and engineers

Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

A 100 g ball moving to the right at 4.0 m/s catches up and collides with a 400 g ball that is moving to the right at 1.0 m/s. If the collision is perfectly elastic, what are the speed and direction of each ball after the collision?
A 20 g ball is fired horizontally with speed v0 toward a 100 g ball hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 100 g ball swings out to a maximum angle θmax = 50°. What was v0 ?
A 30 ton rail car and a 90 ton rail car, initially at rest, are connected together with a giant but massless compressed spring between them. When released, the 30 ton car is pushed away at a speed of 4.0 m/s relative to the 90 ton car. What is the speed of the 30 ton car relative to the ground?
A 500 g particle has velocity vx = -5.0 m/s at t = -2 s. Force Fx = (4 - t 2) N, where t is in s, is exerted on the particle between t = -2 s and t = 2 s. This force increases from 0 N at t = -2 s to 4 N at t = 0 s and then back to 0 N at t = 2 s. What is the particle’s velocity at t = 2 s?
Force Fx = (10 N) sin(2πt/4.0 s) is exerted on a 250 g particle during the interval 0s ≤ t ≤ 2.0s. If the particle starts from rest, what is its speed at t = 2.0 s?
Ann (mass 50 kg) is standing at the left end of a 15-m-long, 500 kg cart that has frictionless wheels and rolls on a frictionless track. Initially both Ann and the cart are at rest. Suddenly, Ann starts running along the cart at a speed of 5.0 m/s relative to the cart. How far will Ann have run
The stoplight had just changed and a 2000 kg Cadillac had entered the intersection, heading north at 3.0 m/s, when it was struck by a 1000 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35° north of east. How fast was the Volkswagen going just before
In FIGURE P11.57, a block of mass m slides along a frictionless track with speed vm. It collides with a stationary block of mass M. Find an expression for the minimum value of vmthat will allow the second block to circle the loop-the-loop without falling off if the collision is(a) Perfectly
You have been asked to design a “ballistic spring system” to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the
A 100 g granite cube slides down a 40° frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 200 g steel cube at rest. How high above the table should the granite cube be released to give the steel cube a speed of 150 cm/s?
Two 500 g blocks of wood are 2.0 m apart on a frictionless table. A 10 g bullet is fired at 400 m/s toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 6.0 m/s. What is the speed of the
In a ballistics test, a 25 g bullet traveling horizontally at 1200 m/s goes through a 30-cm-thick 350 kg stationary target and emerges with a speed of 900 m/s. The target is free to slide on a smooth horizontal surface. What is the target’s speed just after the bullet emerges?
A 1500 kg weather rocket accelerates upward at 10 m/s2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the
An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2 m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction.
You are part of a search-and-rescue mission that has been called out to look for a lost explorer. You€™ve found the missing explorer, but, as FIGURE P11.50 shows, you€™re separated from him by a 200-m-high cliff and a 30-m-wide raging river. To save his life, you need to get a
a. A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk. Find an expression for the bullet’s speed vbullet.b. What is the speed of a 10 g bullet that, when
One billiard ball is shot east at 2.0 m/s. A second, identical billiard ball is shot west at 1.0 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90° and sending it north at 1.41 m/s. What are the speed and direction of the first ball after the
A firecracker in a coconut blows the coconut into three pieces.Two pieces of equal mass fly off south and west, perpendicular to each other, at speed v0. The third piece has twice the mass as the other two. What are the speed and direction of the third piece?Give the direction as an angle east of
Squids rely on jet propulsion to move around. A 1.50 kg squid (including the mass of water inside the squid) drifting at 0.40 m/s suddenly ejects 0.10 kg of water to get itself moving at 2.50 m/s. If drag is ignored over the small interval of time needed to expel the water (the impulse
Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass of 1.0 × 1013 kg hits the
Air-track gliders with masses 300 g, 400 g, and 200 g are lined up and held in place with lightweight springs compressed between them. All three are released at once. The 200 g glider flies off to the right while the 300 g glider goes left. Their position-versus-time graphs, as measured by motion
A particle of mass m is at rest at t = 0. Its momentum for t > 0 is given by px = 6t2 kg m/s, where t is in s. Find an expression for Fx (t), the force exerted on the particle as a function of time.
The flowers of the bunchberry plant open with astonishing force and speed, causing the pollen grains to be ejected out of the flower in a mere 0.30 ms at an acceleration of 2.5 × 104 m/s2. If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of 1.0 × 10-7 g?
A 200 g ball is dropped from a height of 2.0 m, bounces on a hard floor, and rebounds to a height of 1.5 m. FIGURE P11.41 shows the impulse received from the floor. What maximum force does the floor exert on the ball? F, Fmax -t (ms) 5.0 ms' FIGURE P11.41
A 500 g cart is released from rest 1.00 m from the bottom of a frictionless, 30.0° ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. FIGURE P11.40 shows the force during the collision. After the cart bounces, how far does it roll back up the ramp? F; (N) 200 -t
A 60 g tennis ball with an initial speed of 32 m/s hits a wall and rebounds with the same speed. FIGURE P11.39 shows the force of the wall on the ball during the collision.What is the value of Fmax, the maximum value of the contact force during the collision? F, Fmax Tt (ms) 0+ 4 FIGURE P11.39
A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s.a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the
A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times the mass of the empty rocket. What is the rocket’s speed when half the fuel has been burned?
A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. What mass of fuel is needed to reach a top speed of 4000 m/s?
A 250 g ball collides with a wall. FIGURE EX11.13 shows the ball€™s velocity and the force exerted on the ball by the wall. What is vfx, the ball€™s rebound velocity? F, (N) V, (m/s) 500 - VEr 8.0 ms -10- FIGURE EX11.13
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.9. What are the object€™s speed and direction after the force ends? F, (N) 8. t (s) 0.50 s -8 FIGURE EX11.9
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.8. What are the object€™s speed and direction after the force ends? F, (N) 1.0 s - t (s) -2 - FIGURE EX11.8
A small rocket with 15 kN thrust burns 250 kg of fuel in 30 s. What is the exhaust speed of the hot gases?
At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s.a. How long will it take them to glide to the edge of the rink?b. Where will they reach it? Give your answer as an angle
A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g ball of clay? Give your answer as an angle north of east.
An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors. P, (kg m/s) 2- Pz (kg m/s) FIGURE EX11.32 -2
Two particles collide and bounce apart. FIGURE EX11.31 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of particle 1? Write your answer using unit vectors. P, (kg m/s) 2- |(P.)2 (P -Pz (kg m/s) 4 -2 -4 (P)2 -2- FIGURE EX11.31 2.
A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end of the tube with speed v0. With what speed does the lighter ball emerge from the other end?
Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 s, how long does the lighter skater take to reach the edge?
Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground?Dan’s mass is 50 kg and the skateboard’s mass is 5.0 kg.
A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player’s speed afterward if the ball is thrown ata. 15.0 m/s relative to the ground?b. 15.0 m/s relative to the player?
A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer?
package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.25 to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute.a.
A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface.a. What is the speed of the brick after the collision?b. What percentage of the mechanical energy is lost in this collision?
A proton is traveling to the right at 2.0 × 107 m/s. It has a headon perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the speed and direction of each after the collision?
A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision?
Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football
A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?
The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1.0 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 1000 kg Volkswagen head-on into the Cadillac and save the children. With what speed should you impact
A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately after swallowing?
Three identical train cars, coupled together, are rolling east at speed v0. A fourth car traveling east at 2v0 catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What
A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the glider’s velocity just after the skydiver lets go?
A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?
A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the car’s speed is 20 m/s. What mass of water has collected in the car?
Two balls of clay of known masses hang from the ceiling on massless strings of equal length. They barely touch when both hang at rest. One ball is pulled back until its string is at 45°, then released. It swings down, collides with the second ball, and they stick together. To determine the angle
A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.12 shows the glider€™s velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring? F, (N) V, (m/s) 36 3 - t (s) t (s) Δt -3 FIGURE EX11.12
Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula.a. Which skater, if either, has the greater momentum after the push-off? Explain.b. Which skater, if either, has the greater speed after the push-off? Explain.
Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these 30 s is negligible. a. What impulse does the engine impart to the rocket?b. At what time does the
Two particles collide, one of which was initially moving and the other initially at rest.a. Is it possible for both particles to be at rest after the collision? Give an example in which this happens, or explain why it can’t happen.b. Is it possible for one particle to be at rest after the
A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the momentum principle to find how long the sled takes to travel from A to B.
Suppose a rubber ball collides head-on with a more massive steel ball traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.
A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify “the system.”
Automobiles are designed with “crumple zones” intended to collapse in a collision. Use the ideas of this chapter to explain why.
FIGURE EX11.7 is an incomplete momentum bar chart for a 50 g particle that experiences an impulse lasting 10 ms. What were the speed and direction of the particle before the impulse? kg m/s -2 -4- J. Pir Pir + FIGURE EX11.7
It feels better to catch a hard ball while wearing a padded glove than to catch it bare handed. Use the ideas of this chapter to explain why.
FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object? kg m/s 2 - 0- -2 - -4- J. Pir + Pix FIGURE EX11.6 | |
Angie, Brad, and Carlos are discussing a physics problem in which two identical bullets are fired with equal speeds at equal mass wood and steel blocks resting on a frictionless table. One bullet bounces off the steel block while the second becomes embedded in the wood block. “All the masses and
In FIGURE EX11.5, what value of Fmaxgives an impulse of 6.0 N s? F, max 0+ 2 t (ms) 10 4 8. FIGURE EX11.5
A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 m, starting from rest. After traveling 1 m, is the momentum of the plastic cart greater than, less than, or equal to the momentum
What is the impulse on a 3.0 kg particle that experiences the force shown in FIGURE EX11.4? F, (N) 2000 - 1500 1000 500 0+ 0 2 4 6 8 10 12 -t (ms) FIGURE EX11.4
A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. After the force is removed at t = 1 s, is the momentum of the plastic cart greater than, less than, or equal to
What impulse does the force shown in FIGURE EX11.3 exert on a 250 g particle? F, (N) 1000- -t (ms) 6. 0+ 2 4 FIGURE EX11.3
A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of -4 N s. What are the object’s speed and direction after the impulse?
What is the magnitude of the momentum ofa. A 3000 kg truck traveling at 15 m/s?b. A 200 g baseball thrown at 40 m/s?
A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 N s. What are the object’s speed and direction after the impulse?
At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?
Rank in order, from largest to smallest, the momenta (px)ato (px)eof the objects in FIGURE Q11.1. 20 g 20 g 200 g b 2 m/s 1 m/s 0.1 m/s 10 g 10 g 1 m/s 2 m/s FIGURE Q11.1
A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE CP10.74. a. Find an expression for the sled??s speed when it is at angle ϕ.b. Use Newton??s laws to find the maximum speed the sled can have at angle ϕ without leaving the surface.c. At what
The spring in FIGURE CP10.73 has a spring constant of 1000 N/m. It is compressed 15 cm, then launches a 200 g block. The horizontal surface is frictionless, but the block€™s coefficient of kinetic friction on the incline is 0.20. What distance d does the block sail through the air? 2.0 m
A 10 kg box slides 4.0 m down the frictionless ramp shown in FIGURE CP10.72, then collides with a spring whose spring constant is 250 N/m. a. What is the maximum compression of the spring?b. At what compression of the spring does the box have its maximum speed? 4.0 m 30° FIGURE CP10.72
It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40
In a physics lab experiment, a compressed spring launches a 20 g metal ball at a 30° angle. Compressing the spring 20 cm causes the ball to hit the floor 1.5 m below the point at which it leaves the spring after traveling 5.0 m horizontally. What is the spring constant?
A pendulum is formed from a small ball of mass m on a string of length L. As FIGURE CP10.69 shows, a peg is height h = L/3 above the pendulum€™s lowest point. From what minimum angle Î¸ must the pendulum be released in order for the ball to go over the top of the peg without
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial representation.c. Finish the solution of the problem.1/2 (0.50 kg)vf2 + (0.50 kg)(9.80 m/s2)(0 m)+ 1/2 (400
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial representation.c. Finish the solution of the problem.1/2 (0.20 kg)(2.0 m/s)2 + 1/2 k1(0 m)2= 1/2 (0.20 kg)(0
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial representation.c. Finish the solution of the problem.1/2 (1500 kg)(5.0 m/s)2 + (1500 kg)(9.80 m/s2)(10 m)= 1/2
Write a realistic problem for which the energy bar chart shown in FIGURE P10.65 correctly shows the energy at the beginning and end of the problem. E (J) 40 20 -20 - K; + UGi+ Uspi = K¡ + Ugf+Uspf FIGURE P10.65 | |
An object moving in the xy-plane is subjected to the force Fu = (2xy î + 3y ĵ) N, where x and y are in m.a. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?b. The
An object moving in the xy-plane is subjected to the force F = (2xy î + x2 ĵ) N, where x and y are in m.a. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?b. The
A particle that can move along the x-axis experiences an interaction force Fx = (3x2 - 5x) N, where x is in m. Find an expression for the system’s potential energy.
The potential energy for a particle that can move along the x-axis is U = Ax2 + B sin(πx/L), where A, B, and L are constants. What is the force on the particle at(a) x = 0,(b) x = L/2,(c) x = L?
A clever engineer designs a “sprong” that obeys the force law Fx = -q(x - xeq)3, where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we’ll let xeq = 0 m. Then Fx = -qx3.a. What are the units of q?b. Find an expression for the potential
A 100 g particle experiences the one-dimensional, conservative force Fxshown in FIGURE P10.59.a. Let the zero of potential energy be at x = 0 m. What is the potential energy at x = 1.0, 2.0, 3.0, and 4.0 m?b. Suppose the particle is shot to the right from x = 1.0 m with a speed of 25 m/s. Where is
A particle that can move along the x-axis is part of a system with potential energywhere A and B are positive constants.a. Where are the particle€™s equilibrium positions?b. For each, is it a point of stable or unstable equilibrium? A B U(x) = х? х
A system has potential energy U(x) = x + sin((2 rad/m)x) as a particle moves over the range 0 m ≤ x ≤ π m.a. Where are the equilibrium positions in this range?b. For each, is it a point of stable or unstable equilibrium?
A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx = (20 - 5x) N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially the block is at rest at x = 0 m. What is the block’s speed when it has been pulled to x = 4.0 m?
Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons€”hence its name. But the
The spring shown in FIGURE P10.54 is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student??s coefficient of kinetic friction on the 30? incline is 0.15. a. What is the student??s speed just after losing contact with the
a. A 50 g ice cube can slide without friction up and down a 30° slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ice cube is released, what total distance will it travel up the slope before reversing
Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if (a) The coefficient of kinetic friction for the block on the table is μk (b) The table is frictionless. M m h FIGURE P10.52

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