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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

What is the momentum of an automobile (weight = 9800 N) when it is moving at 35 m/s to the south?
A submarine of mass 2.5 × 106 kg and initially at rest fires a torpedo of mass 250 kg. The torpedo has an initial speed of 100.0 m/s. What is the initial recoil speed of the submarine? Neglect the drag force of the water?
A uranium nucleus (mass 238 u), initially at rest, undergoes radioactive decay. After an alpha particle (mass 4.0 u) is emitted, the remaining nucleus is thorium (mass 234 u). If the alpha particle is moving at 0.050 times the speed of light, what is the recoil speed of the thorium nucleus? ("u" is
Dash is standing on his frictionless skateboard with three balls, each with a mass of 100 g, in his hands. The combined mass of Dash and his skateboard is 60 kg. How fast should dash throw the balls forward if he wants to move backward with a speed of 0.50 m/s? Do you think Dash can succeed?
A 58-kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720-g socket wrench with a velocity of 5.0 m/s in a direction away from the ship. After 0.50 s,
A man with a mass of 65 kg skis down a frictionless hill that is 5.0 m high. At the bottom of the hill the terrain levels out. As the man reaches the horizontal section, he grabs a 20-kg backpack and skis off a 2.0-m-high ledge. At what horizontal distance from the edge of the ledge does the man
A cannon on a railroad car is facing in a direction parallel to the tracks. It fires a 98-kg shell at a speed of 105 m/s (relative to the ground) at an angle of 60.0° above the horizontal. If the cannon plus car have a mass of 5.0 × 104 kg, what is the recoil speed of the car if it was at rest
A marksman standing on a motionless railroad car fires a gun into the air at an angle of 30.0° from the horizontal. The bullet has a speed of 173 m/s (relative to the ground) and a mass of 0.010 kg. The man and car move to the left at a speed of 1.0 Ã— 10ˆ’3 m/s after he
Particle A is at the origin and has a mass of 30.0 g. Particle B has a mass of 10.0 g. Where must particle B be located if the coordinates of the cm are (x, y) = (2.0 cm, 5.0 cm)?
Particle A has a mass of 5.0 g and particle B has a mass of 1.0 g. Particle A is located at the origin and particle B is at the point (x, y) = (25 cm, 0). What is the location of the cm?
The three bodies in the figure each have the same mass. If one of the bodies is moved 12 cm in the positive x -direction, by how much does the cm move?
Verify that the SI unit of impulse is the same as the SI unit of momentum?
The positions of three particles, written as (x, y) coordinates, are: particle 1 (mass 4.0 kg) at (4.0 m, 0 m); particle 2 (mass 6.0 kg) at (2.0 m, 4.0 m); particle 3 (mass 3.0 kg) at (−1.0 m, − 2.0 m). What is the location of the cm?
Belinda needs to find the cm of a sculpture she has made so that it will hang in a gallery correctly. The sculpture is all in one plane and consists of various shaped uniform objects with masses and sizes as shown. Where is the cm of this sculpture? Assume the thin rods connecting the larger pieces
Jane is sitting on a chair with her lower leg at a 30.0° angle with respect to the vertical, as shown. You need to develop a computer model of her leg to assist in some medical research. If you assume that her leg can be modeled as two uniform cylinders, one with mass M = 20 kg and length L =
Find the x-coordinate of the cm of the composite object shown in the figure. The sphere, cylinder, and rectangular solid all have a uniform composition. Their masses and dimensions are: sphere: 200 g, diameter = 10 cm; cylinder: 450 g, length = 17 cm, radius = 5.0 cm; rectangular solid: 325 g,
Consider two falling bodies. Their masses are 3.0 kg and 4.0 kg. At time t = 0, the two are released from rest. What is the velocity of their cm at t = 10.0 s? Ignore air resistance.
Body A of mass 3 kg is moving in the + x -direction with a speed of 14 m/s. Body B of mass 4 kg is moving in the − y -direction with a speed of 7 m/s. What are the x - and y -components of the velocity of the cm of the two bodies?
If a particle of mass 5.0 kg is moving east at 10 m/s and a particle of mass 15 kg is moving west at 10 m/s, what is the velocity of the cm of the pair?
An object located at the origin and having mass M explodes into three pieces having masses M /4, M /3, and 5 M /12. The pieces scatter on a horizontal frictionless xy -plane. The piece with mass M /4 flies away with velocity 5.0 m/s at 37° above the x -axis. The piece with mass M /3 has velocity
Prove Eq. (7-13) Î£ext = M CM. Start with Î£ext = where Î£ext is the net external force acting on a system and is the total momentum of the system?
A helium atom (mass 4.00 u) moving at 618 m/s to the right collides with an oxygen molecule (mass 32.0 u) moving in the same direction at 412 m/s. After the collision, the oxygen molecule moves at 456 m/s to the right. What is the velocity of the helium atom after the collision?
A cue stick hits a cue ball with an average force of 24 N for a duration of 0.028 s. If the mass of the ball is 0.16 kg, how fast is it moving after being struck?
A toy car with a mass of 120 g moves to the right with a speed of 0.75 m/s. A small child drops a 30.0-g piece of clay onto the car. The clay sticks to the car and the car continues to the right. What is the change in speed of the car? Consider the frictional force between the car and the ground to
In the railroad freight yard, an empty freight car of mass m rolls along a straight level track at 1.0 m/s and collides with an initially stationary, fully loaded boxcar of mass 4.0 m. The two cars couple together on collision. (a) What is the speed of the two cars after the collision? (b) Suppose
A 0.020-kg bullet traveling at 200.0 m/s east hits a motionless 2.0-kg block and bounces off it, retracing its original path with a velocity of 100.0 m/s west. What is the final velocity of the block? Assume the block rests on a perfectly frictionless horizontal surface.
A block of wood of mass 0.95 kg is initially at rest. A bullet of mass 0.050 kg traveling at 100.0 m/s strikes the block and becomes embedded in it. With what speed do the block of wood and the bullet move just after the collision?
A 0.020-kg bullet is shot horizontally and collides with a 2.00-kg block of wood. The bullet embeds in the block and the block slides along a horizontal surface for 1.50 m. If the coefficient of kinetic friction between the block and surface is 0.400, what was the original speed of the bullet?
A 2.0-kg block is moving to the right at 1.0 m/s just before it strikes and sticks to a 1.0-kg block initially at rest. What is the total momentum of the two blocks after the collision?
A 75-kg man is at rest on ice skates. A 0.20-kg ball is thrown to him. The ball is moving horizontally at 25 m/s just before the man catches it. How fast is the man moving just after he catches the ball?
A BMW of mass 2.0 × 103 kg is traveling at 42 m/s. It approaches a 1.0 × 103 kg Volkswagen going 25 m/s in the same direction and strikes it in the rear. Neither driver applies the brakes. Neglect the relatively small frictional forces on the cars due to the road and due to air resistance. (a) If
A 100-g ball collides elastically with a 300-g ball that is at rest. If the 100-g ball was traveling in the positive x - direction at 5.00 m/s before the collision, what are the velocities of the two balls after the collision?
A projectile of 1.0-kg mass approaches a stationary body of 5.0 kg at 10.0 m/s and, after colliding, rebounds in the reverse direction along the same line with a speed of 5.0 m/s. What is the speed of the 5.0-kg body after the collision?
A system consists of three particles with these masses and velocities: mass 3.0 kg, moving north at 3.0 m/s; mass 4.0 kg, moving south at 5.0 m/s; and mass 7.0 kg, moving north at 2.0 m/s. What is the total momentum of the system?
A 2.0-kg object is at rest on a perfectly frictionless surface when it is hit by a 3.0-kg object moving at 8.0 m/s. If the two objects are stuck together after the collision, what is the speed of the combination?
A spring of negligible mass is compressed between two blocks, A and B, which are at rest on a frictionless horizontal surface at a distance of 1.0 m from a wall on the left and 3.0 m from a wall on the right. The sizes of the blocks and spring are small. When the spring is released, block A moves
Two identical gliders on an air track are held together by a piece of string, compressing a spring between the gliders. While they are moving to the right at a common speed of 0.50 m/s, someone holds a match under the string and burns it, letting the spring force the gliders apart. One glider is
A 0.010-kg bullet traveling horizontally at 400.0 m/s strikes a 4.0-kg block of wood sitting at the edge of a table. The bullet is lodged into the wood. If the table height is 1.2 m, how far from the table does the block hit the floor?
Two objects with masses m1 and m2 approach each other with equal and opposite momentum so that the total momentum is zero. Show that, if the collision is elastic, the final speed of each object must be the same as its initial speed. (The final velocity of each object is not the same as its initial
A 6.0-kg object is at rest on a perfectly frictionless surface when it is struck head-on by a 2.0-kg object moving at 10 m/s. If the collision is perfectly elastic, what is the speed of the 6.0-kg object after the collision?
Show that in any elastic collision between two objects, the relative speed of the two is the same before and after the collision. [Look at the collision in its cm frame -the reference frame in which the cm is at rest. The relative speed of two objects is the same in any inertial reference frame.]
A firecracker is tossed straight up into the air. It explodes into three pieces of equal mass just as it reaches the highest point. Two pieces move off at 120 m/s at right angles to each other. How fast is the third piece moving?
Body A of mass M has an original velocity of 6.0 m/s in the + x -direction toward a stationary body (body B) of the same mass. After the collision, body A has velocity components of 1.0 m/s in the + x -direction and 2.0 m/s in the + y -direction. What is the magnitude of body B's velocity after the
(a) With reference to Practice Problem 7.11, find the momentum change of the ball of mass m1 during the collision. Give your answer in x - and y -component form; express the components in terms of m1 and vi. (b) Repeat for the ball of mass m2. How are the momentum changes related?
A sports car traveling along a straight line increases its speed from 20.0 mi/h to 60.0 mi/h? (a) What is the ratio of the final to the initial magnitude of its momentum? (b) What is the ratio of the final to the initial kinetic energy?
A hockey puck moving at 0.45 m/s collides elastically with another puck that was at rest. The pucks have equal mass. The first puck is deflected 37° to the right and moves off at 0.36 m/s. Find the speed and direction of the second puck after the collision?
Puck 1 sliding along the x -axis strikes stationary puck 2 of the same mass. After the elastic collision, puck 1 moves off at speed v1f in the direction 60.0° above the x-axis; puck 2 moves off at speed v2f in the direction 30.0° below the x -axis. Find v2f in terms of v1f?
Block A, with a mass of 220 g, is traveling north on a frictionless surface with a speed of 5.0 m/s. Block B, with a mass of 300 g travels west on the same surface until it collides with A. After the collision, the blocks move off together with a velocity of 3.13 m/s at an angle of 42.5° to the
A projectile of mass 2.0 kg approaches a stationary target body at 5.0 m/s. The projectile is deflected through an angle of 60.0 ° and its speed after the collision is 3.0 m/s. What is the magnitude of the momentum of the target body after the collision?
A 1500-kg car moving east at 17 m/s collides with a 1800-kg car moving south at 15 m/s and the two cars stick together. (a) What is the velocity of the cars right after the collision? (b) How much kinetic energy was converted to another form during the collision?
A car with a mass of 1700 kg is traveling directly northeast (45° between north and east) at a speed of 14 m/s (31 mph), and collides with a smaller car with a mass of 1300 kg that is traveling directly south at a speed of 18 m/s (40 mph). The two cars stick together during the collision. With
In a nuclear reactor, a neutron moving at speed vi in the positive x-direction strikes a deuteron, which is at rest. The neutron is deflected by 90.0° and moves off with speed vi / √3̅ in the positive y-direction. Find the x-and y -components of the deuteron's velocity after the collision. (The
Two identical pucks are on an air table. Puck A has an initial velocity of 2.0 m/s in the + x -direction. Puck B is at rest. Puck A collides elastically with puck B and A moves off at 1.0 m/s at an angle of 60° above the x-axis. What is the speed and direction of puck B after the collision?
In a circus trapeze act, two acrobats actually fly through the air and grab on to one another, then together grab a swinging bar. One acrobat, with a mass of 60 kg, is moving at 3.0 m/s at an angle of 10° above the horizontal and the other, with a mass of 80 kg, is approaching her with a speed of
Two African swallows fly toward one another, carrying coconuts. The first swallow is flying north horizontally with a speed of 20 m/s. The second swallow is flying at the same height as the first and in the opposite direction with a speed of 15 m/s. The mass of the first swallow is 0.270 kg and the
A ball of mass 5.0 kg moving with a speed of 2.0 m/s in the + x -direction hits a wall and bounces back with the same speed in the − x -direction. What is the change of momentum of the ball?
A sled of mass 5.0 kg is coasting along on a frictionless ice-covered lake at a constant speed of 1.0 m/s. A 1.0-kg book is dropped vertically onto the sled. At what speed does the sled move once the book is on it?
An automobile weighing 13.6 kN is moving at 17.0 m/s when it collides with a stopped car weighing 9.0 kN. If they lock bumpers and move off together, what is their speed just after the collision?
For a system of three particles moving along a line, an observer in a laboratory measures the following masses and velocities. What is the velocity of the cm of the system? Mass (kg) vx (m/s) 3.0 .......................+290 5.0 .......................−120 2.0 .......................+52
An intergalactic spaceship is traveling through space far from any planets or stars, where no human has gone before. The ship carries a crew of 30 people (of total mass 2.0 × 103 kg). If the speed of the spaceship is 1.0 × 105 m/s and its mass (excluding the crew) is 4.8 × 104 kg, what is the
A baseball player pitches a fastball toward home plate at a speed of 41 m/s. The batter swings, connects with the ball of mass 145 g, and hits it so that the ball leaves the bat with a speed of 37 m/s. Assume that the ball is moving horizontally just before and just after the collision with the
A tennis ball of mass 0.060 kg is served. It strikes the ground with a velocity of 54 m/s (120 mi/h) at an angle of 22° below the horizontal. Just after the bounce it is moving at 53 m/s at an angle of 18° above the horizontal. If the interaction with the ground lasts 0.065 s, what average force
A uniform rod of length 30.0 cm is bent into the shape of an inverted U. Each of the three sides is of length 10.0 cm. Find the location, in x - and y - coordinates, of the cm as measured from the origin.
A child places 12 wooden blocks together, as shown in the figure. If each block has the same mass and density, where is the cm of these blocks? Each block is a cube with sides of 1.0 inch length. The origin of the coordinate system is at the center of the farthest block to the left.
To contain some unruly demonstrators, the riot squad approaches with fire hoses. Suppose that the rate of flow of water through a fire hose is 24 kg/s and the stream of water from the hose moves at 17 m/s. What force is exerted by such a stream on a person in the crowd? Assume that the water comes
An inexperienced catcher catches a 130 km/h fastball of mass 140 g within 1 ms, whereas an experienced catcher slightly retracts his hand during the catch, extending the stopping time to 10 ms. What are the average forces imparted to the two gloved hands during the catches?
An object of mass 3.0 kg is projected into the air at a 55° angle. It hits the ground 3.4 s later. What is its change in momentum while it is in the air? Ignore air resistance.
A stationary 0.1-g fly encounters the windshield of a 1000-kg automobile traveling at 100 km/h. (a) What is the change in momentum of the car due to the fly? (b) What is the change of momentum of the fly due to the car? (c) Approximately how many flies does it take to reduce the car's speed by 1
A 0.15-kg baseball is pitched with a speed of 35 m/s (78 mph). When the ball hits the catcher's glove, the glove moves back by 5.0 cm (2 in.) as it stops the ball. (a) What was the change in momentum of the baseball? (b) What impulse was applied to the baseball? (c) Assuming a constant acceleration
A projectile of mass 2.0 kg approaches a stationary target body at 8.0 m/s. The projectile is deflected through an angle of 90.0° and its speed after the collision is 6.0 m/s. What is the speed of the target body after the collision if the collision is perfectly elastic?
A radioactive nucleus is at rest when it spontaneously decays by emitting an electron and neutrino. The momentum of the electron is 8.20 × 10−19 kg·m/s and it is directed at right angles to that of the neutrino. The neutrino's momentum has magnitude 5.00 × 10 − 19 kg·m/s. (a) In what
A 60.0-kg woman stands at one end of a 120-kg raft that is 6.0 m long. The other end of the raft is 0.50 m from a pier. (a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the raft and the pier? (b) In (a), how far did
A police officer is investigating the scene of an accident where two cars collided at an intersection. One car with a mass of 1100 kg moving west had collided with a 1300-kg car moving north. The two cars, stuck together, skid at an angle of 30° north of west for a distance of 17 m. The
A jet plane is flying at 130 m/s relative to the ground. There is no wind. The engines take in 81 kg of air per second. Hot gas (burned fuel and air) is expelled from the engines at high speed. The engines provide a forward force on the plane of magnitude 6.0 × 104 N. At what speed relative to the
Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass 0.01 pg (10ˆ’17 kg) from 0 to 1
The pendulum bobs in the figure are made of soft clay so that they stick together after impact. The mass of bob A is half that of bob B. Bob B is initially at rest. What is the ratio of the kinetic energy of the combined bobs, just after impact, to the kinetic energy of bob A just before impact?
The pendulum bobs in the figure are made of soft clay so that they stick together after impact. The mass of bob A is half that of bob B. Bob B is initially at rest. If bob A is released from a height h above its lowest point, what is the maximum height attained by bobs A and B after the collision?
An object of mass 3.0 kg is allowed to fall from rest under the force of gravity for 3.4 s. What is the change in its momentum? Ignore air resistance.
A flat, circular metal disk of uniform thickness has a radius of 3.0 cm. A hole is drilled in the disk that is 1.5 cm in radius. The hole is tangent to one side of the disk. Where is the cm of the disk now that the hole has been drilled? [The original disk (before the hole is drilled) can be
Two pendulum bobs have equal masses and lengths (5.1 m). Bob A is initially held horizontally while bob B hangs vertically at rest. Bob A is released and collides elastically with bob B. How fast is bob B moving immediately after the collision?
Two identical gliders, each with elastic bumpers and mass 0.10 kg, are on a horizontal air track. Friction is negligible. Glider 2 is stationary. Glider 1 moves toward glider 2 from the left with a speed of 0.20 m/s. They collide. After the collision, what are the velocities of glider 1 and glider
A radium nucleus (mass 226 u) at rest decays into a radon nucleus (symbol Rn, mass 222 u) and an alpha particle (symbol a, mass 4 u). (a) Find the ratio of the speeds va / vRn after the decay. (b) Find the ratio of the magnitudes of the momenta p a / pR. (c) Find the ratio of the kinetic energies
A planet moves around the Sun in an elliptical orbit. (a) Show that the external torque acting on the planet about an axis through the Sun is zero? (b) Since the torque is zero, the planet's angular momentum is constant. Write an expression for the planet's angular momentum in terms of its mass m,
A 68-kg woman stands straight with both feet flat on the floor. Her center of gravity is a horizontal distance of 3.0 cm in front of a line that connects her two ankle joints. The Achilles tendon attaches the calf muscle to the foot a distance of 4.4 cm behind the ankle joint. If the Achilles
A merry-go-round (radius R, rotational inertia Ii) spins with negligible friction. Its initial angular velocity is (i. A child (mass m) on the merry-go-round moves from the center out to the rim. (a) Calculate the angular velocity after the child moves out to the rim. (b) Calculate the rotational
Since humans are generally not symmetrically shaped, the height of our center of gravity is generally not half of our height. One way to determine the location of the center of gravity is shown in the diagram. A 2.2-m-long uniform plank is supported by two bathroom scales, one at either end.
A spool of thread of mass m rests on a plane inclined at angle (. The end of the thread is tied as shown. The outer radius of the spool is R and the inner radius (where the thread is wound) is r. The rotational inertia of the spool is I. Give all answers in terms of m, (, R, r, I, and g. (a) If
A bicycle travels up an incline at constant velocity. The magnitude of the frictional force due to the road on the rear wheel is f = 3.8 N. The upper section of chain pulls on the sprocket wheel, which is attached to the rear wheel, with a force . The lower section of chain is slack. If the radius
A circus roustabout is attaching the circus tent to the top of the main support post of length L when the post suddenly breaks at the base. The worker's weight is negligible relative to that of the uniform post. What is the speed with which the roustabout reaches the ground if(a) He jumps at the
A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.50 rev/s. The student on the platform then pulls the dumbbells
A person places his hand palm downward on a scale and pushes down on the scale until it reads 96 N. The triceps muscle is responsible for this arm extension force. Find the force exerted by the triceps muscle. The bottom of the triceps muscle is 2.5 cm to the left of the elbow joint and the palm is
The posture of small animals may prevent them from being blown over by the wind. For example, with wind blowing from the side, a small insect stands with bent legs; the more bent the legs, the lower the body and the smaller the angle (. The wind exerts a force on the insect, which causes a torque
(a) Redo Example 8.7 to find an algebraic solution for d in terms of M, m, (s, L, and q. (b) Use this expression to show that placing the ladder at a larger angle q (that is, more nearly vertical) enables the person to climb farther up the ladder without having it slip, all other things being
A child of mass 40.0 kg is sitting on a horizontal seesaw at a distance of 2.0 m from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?
A 124-g mass is placed on one pan of a balance, at a point 25 cm from the support of the balance. What is the magnitude of the torque about the support exerted by the mass?
A uniform door weighs 50.0 N and is 1.0 m wide and 2.6 m high. What is the magnitude of the torque due to the door's own weight about a horizontal axis perpendicular to the door and passing through a corner?
A tower outside the Houses of Parliament in London has a famous clock commonly referred to as Big Ben, the name of its 13-ton chiming bell. The hour hand of each clock face is 2.7 m long and has a mass of 60.0 kg. Assume the hour hand to be a uniform rod attached at one end. (a) What is the torque
Any pair of equal and opposite forces acting on the same object is called a couple. Consider the couple in part (a) of the figure. The rotation axis is perpendicular to the page and passes through point P. (a) Show that the net torque due to this couple is equal to Fd, where d is the distance
A 46.4-N force is applied to the outer edge of a door of width 1.26 m in such a way that it acts (a) Perpendicular to the door, (b) At an angle of 43.0 ° with respect to the door surface, (c) So that the line of action of the force passes through the axis of the door hinges. Find the torque for
A trap door, of length and width 1.65 m, is held open at an angle of 65.0° with respect to the floor. A rope is attached to the raised edge of the door and fastened to the wall behind the door in such a position that the rope pulls perpendicularly to the trap door. If the mass of the trap door is

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