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physics
mechanics

Questions and Answers of Mechanics

In the What If? Section of Example 4.7, it was claimed that the maximum range of a ski-jumper occurs for a launch angle ' given by Where is the angle that the hill makes with the horizontal in
1. A 3.00-kg particle has a velocity of (3.00i = 4.00j) m/s. (a) Find its x and y components of momentum. (b) Find the magnitude and direction of its momentum.
A 0.100-kg ball is thrown straight up into the air with an initial speed of 15.0 m/s. Find the momentum of the ball (a) At its maximum height and (b) Halfway up to its maximum height.
How fast can you set the Earth moving? In particular, when you jump straight up as high as you can, what is the order of magnitude of the maximum recoil speed that you give to the Earth? Model the
Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them (Fig. P9.4).
(a) A particle of mass m moves with momentum p. Show that the kinetic energy of the particle is K = p2/2m. (b) Express the magnitude of the particle’s momentum in terms of its kinetic energy and
A friend claims that, as long as he has his seatbelt on, he can hold on to a 12.0-kg child in a 60.0 mi/h head-on collision with a brick wall in which the car passenger compartment comes to a stop in
An estimated force€“time curve for a baseball struck by a bat is shown in Figure P9.7. From this curve, determine(a) The impulse delivered to the ball,(b) The average force exerted on the
A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?
A 3.00-kg steel ball strikes a wall with a speed of 10.0 m/s at an angle of 60.0° with the surface. It bounces off with the same speed and angle (Fig. P9.9). If the ball is in contact with the
A tennis player receives a shot with the ball (0.060 0 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a)
In a slow-pitch softball game, a 0.200-kg softball crosses the plate at 15.0 m/s at an angle of 45.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 40.0
A professional diver performs a dive from a platform 10 m above the water surface. Estimate the order of magnitude of the average impact force she experiences in her collision with the water. State
A garden hose is held as shown in Figure P9.13. The hose is originally full of motionless water. What additional force is necessary to hold the nozzle stationary after the water flow is turned on, if
A glider of mass m is free to slide along a horizontal air track. It is pushed against a launcher at one end of the track. Model the launcher as a light spring of force constant k compressed by a
High-speed stroboscopic photographs show that the head of a golf club of mass 200 g is traveling at 55.0 m/s just before it strikes a 46.0-g golf ball at rest on a tee. After the collision, the club
An archer shoots an arrow toward a target that is sliding toward her with a speed of 2.50 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.0 m/s and passes through the
A 10.0-g bullet is fired into a stationary block of wood (m = 5.00 kg). The relative motion of the bullet stops inside the block. The speed of the bullet-plus-wood combination immediately after the
A railroad car of mass 2.50 X 104 kg is moving with a speed of 4.00 m/s. It collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same
Four railroad cars, each of mass 2.50 X 104 kg, are coupled together and coasting along horizontal tracks at speed vi toward the south. A very strong but foolish movie actor, riding on the second
Two blocks are free to slide along the frictionless wooden track ABC shown in Figure P9.20. The block of mass m1 5.00 kg is released from A. Protruding from its front end is the north pole of a
A 45.0-kg girl is standing on a plank that has a mass of 150 kg. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface. The girl begins to
Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that
A neutron in a nuclear reactor makes an elastic head-on collision with the nucleus of a carbon atom initially at rest. (a) What fraction of the neutron’s kinetic energy is transferred to the
As shown in Figure P9.24, a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of
A 12.0-g wad of sticky clay is hurled horizontally at a 100-g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50 m before coming
A 7.00-g bullet, when fired from a gun into a 1.00-kg block of wood held in a vise, penetrates the block to a depth of 8.00 cm. What If? This block of wood is placed on a frictionless horizontal
(a) Three carts of masses 4.00 kg, 10.0 kg, and 3.00 kg move on a frictionless horizontal track with speeds of 5.00 m/s, 3.00 m/s, and 4.00 m/s, as shown in Figure P9.27. Velcro couplers make the
A 90.0-kg fullback running east with a speed of 5.00 m/s is tackled by a 95.0-kg opponent running north with a speed of 3.00 m/s. If the collision is perfectly inelastic, (a) Calculate the speed
Two shuffleboard disks of equal mass, one orange and the other yellow are involved in an elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with
Two shuffleboard disks of equal mass, one orange and the other yellow are involved in an elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with
The mass of the blue puck in Figure P9.31 is 20.0% greater than the mass of the green one. Before colliding, the pucks approach each other with moment of equal magnitudes and opposite directions, and
Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 m/s toward the east, and the other is traveling north with speed v2i. Neither driver sees the
A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves, at 4.33 m/s, at an angle of 30.0° with respect to the original line of
A proton, moving with a velocity of vi i, collides elastically with another proton that is initially at rest. If the two protons have equal speeds after the collision, find (a) The speed of each
An object of mass 3.00 kg, moving with an initial velocity of 5.00i m/s, collides with and sticks to an object of mass 2.00 kg with an initial velocity of ─3.00j m/s. Find the final velocity of
Two particles with masses m and 3m are moving toward each other along the x axis with the same initial speeds vi. Particle m is traveling to the left, while particle 3m is traveling to the right.
An unstable atomic nucleus of mass 17.0 X 10─27 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.00 X 10─27 kg, moves along the y axis with a speed
Four objects are situated along the y axis as follows: a 2.00 kg object is at + 3.00 m, a 3.00-kg object is at +2.50 m, a 2.50-kg object is at the origin, and a 4.00-kg object is at ─0.500 m.
A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (Fig. P9.39). The angle between the two bonds is 106°. If the bonds are 0.100 nm long, where is the center of mass
The mass of the Earth is 5.98 X 1024 kg, and the mass of the Moon is 7.36 X 1022 kg. The distance of separation, measured between their centers, is 3.84 X 108 m. Locate the center of mass of the
A uniform piece of sheet steel is shaped as in Figure P9.41. Compute the x and y coordinates of the center of mass of the piece.
(a) Consider an extended object whose different portions have different elevations. Assume the free-fall acceleration is uniform over the object. Prove that the gravitational potential energy of the
A rod of length 30.0 cm has linear density (mass-per-length) given by Ǎ = 50.0 g/m + 20.0x g/m2 where x is the distance from one end, measured in meters. (a) What is the mass of the rod? (b)
In the 1968 Olympic Games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the €œFosbury flop.€ It contributed to raising the world
A 2.00-kg particle has a velocity (2.00i ─ 3.00j) m/s, and a 3.00-kg particle has a velocity (1.00i + 6.00j) m/s. Find (a) the velocity of the center of mass and (b) the total momentum of the
Consider a system of two particles in the xy plane: m1 = 2.00 kg is at the location r1 = (1.00i + 2.00j) m and has a velocity of (3.00i + 0.500j) m/s; m2 = 3.00 kg is at r2 = (─4.00i ─
Romeo (77.0 kg) entertains Juliet (55.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade,
A ball of mass 0.200 kg has a velocity of 150i m/s; a ball of mass 0.300 kg has a velocity of ─0.400i m/s. They meet in a head-on elastic collision. (a) Find their velocities after the
The first stage of a Saturn V space vehicle consumed fuel and oxidizer at the rate of 1.50 X 104 kg/s, with an exhaust speed of 2.60 X 103 m/s. (a) Calculate the thrust produced by these engines.
Model rocket engines are sized by thrust, thrust duration, and total impulse, among other characteristics. A size C5 model rocket engine has an average thrust of 5.26 N, a fuel mass of 12.7 g, and an
A rocket for use in deep space is to be capable of boosting a total load (payload plus rocket frame and engine) of 3.00 metric tons to a speed of 10 000 m/s. (a) It has an engine and fuel designed
Rocket Science A rocket has total mass Mi = 360 kg, including 330 kg of fuel and oxidizer. In interstellar space it starts from rest, turns on its engine at time t = 0, and puts out exhaust with
An orbiting spacecraft is described not as a “zero-g,” but rather as a “microgravity” environment for its occupants and for on-board experiments. Astronauts experience slight lurches due to
Two gliders are set in motion on an air track. A spring of force constant k is attached to the near side of one glider. The first glider, of mass m1, has velocity v1, and the second glider, of mass
A 60.0-kg person running at an initial speed of 4.00 m/s jumps onto a 120-kg cart initially at rest (Figure P9.55). The person slides on the cart€™s top surface and finally comes to rest
A golf ball (m = 46.0 g) is struck with a force that makes an angle of 45.0° with the horizontal. The ball lands 200 m away on a flat fairway. If the golf club and ball are in contact for 7.00 ms,
An 80.0-kg astronaut is working on the engines of his ship, which is drifting through space with a constant velocity. The astronaut, wishing to get a better view of the Universe, pushes against the
A bullet of mass m is fired into a block of mass M initially at rest at the edge of a frictionless table of height h (Fig. P9.58). The bullet remains in the block, and after impact the block lands a
A 0.500-kg sphere moving with a velocity (2.00i ─ 3.00j + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with a velocity (─1.00i + 2.00j ─ 3.00k) m/s. (a) If the
A small block of mass m1 = 0.500 kg is released from rest at the top of a curve-shaped frictionless wedge of mass m2 = 3.00 kg, which sits on a frictionless horizontal surface as in Figure P9.60a.
A bucket of mass m and volume V is attached to a light cart, completely covering its top surface. The cart is given a quick push along a straight, horizontal, smooth road. It is raining, so as the
A 75.0-kg firefighter slides down a pole while a constant friction force of 300 N retards her motion. A horizontal 20.0-kg platform is supported by a spring at the bottom of the pole to cushion the
George of the Jungle, with mass m, swings on a light vine hanging from a stationary tree branch. A second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 X 104 N/m, as in
A student performs a ballistic pendulum experiment using an apparatus similar to that shown in Figure 9.11b. She obtains the following average data: h = 8.68 cm, m1 = 68.8 g, and m2 = 263 g. The
Small ice cubes, each of mass 5.00 g, slide down a frictionless track in a steady stream, as shown in Figure P9.66. Starting from rest, each cube moves down through a net vertical distance of 1.50 m
A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure P9.67. The block, initially at rest on a frictionless, horizontal surface, is
Consider as a system the Sun with the Earth in a circular orbit around it. Find the magnitude of the change in the velocity of the Sun relative to the center of mass of the system over a period of 6
There are (one can say) three coequal theories of motion: Newton’s second law, stating that the total force on an object causes its acceleration; the work–kinetic energy theorem, stating that the
A rocket has total mass Mi = 360 kg, including 330 kg of fuel and oxidizer. In interstellar space it starts from rest. Its engine is turned on at time t = 0, and it puts out exhaust with relative
A chain of length L and total mass M is released from rest with its lower end just touching the top of a table, as in Figure P9.71a. Find the force exerted by the table on the chain after the chain
Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as in Figure P9.72 The conveyor belt is supported by frictionless rollers and moves at a constant speed of
A golf club consists of a shaft connected to a club head. The golf club can be modeled as a uniform rod of length L and mass m1 extending radically from the surface of a sphere of radius R and mass
A baseball player holds a 36-oz bat (weight θ 10.0 N) with one hand at the point O (Fig. P12.1). The bat is in equilibrium. The weight of the bat acts along a line 60.0 cm to the right of O.
Write the necessary conditions for equilibrium of the object shown in Figure P12.2. Take the origin of the torque equation at the point O.
A uniform beam of mass mb and length θ supports blocks with masses m1 and m2 at two positions, as in Figure P12.3. The beam rests on two knife edges. For what value of x will the beam be
A circular pizza of radius R has a circular piece of radius R/2 removed from one side as shown in Figure P12.4. The center of gravity has moved from C to C` along the x axis. Show that the distance
A carpenter€™s square has the shape of an L, as in Figure P12.5. Locate its center of gravity.
Pat builds a track for his model car out of wood, as in Figure P12.6. The track is 5.00 cm wide, 1.00m high, and 3.00 m long, and is solid. The runway is cut such that it forms a parabola with the
Consider the following mass distribution: 5.00 kg at (0, 0) m, 3.00 kg at (0, 4.00) m, and 4.00 kg at (3.00, 0) m. Where should a fourth object of mass 8.00 kg be placed so that the center of gravity
Figure P12.8 shows three uniform objects: a rod, a right triangle, and a square. Their masses and their coordinates in meters are given. Determine the center of gravity for the three-object system.
Find the mass m of the counterweight needed to balance the 1 500-kg truck on the incline shown in Figure P12.9. Assume all pulleys are frictionless and mass less.
A mobile is constructed of light rods, light strings, and beach souvenirs, as shown in Figure P12.10. Determine the masses of the objects (a) m1, (b) m2, and (c) m3.
Two pans of a balance are 50.0 cm apart. The fulcrum of the balance has been shifted 1.00 cm away from the center by a dishonest shopkeeper. By what percentage is the true weight of the goods being
A 20.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in Figure P12.12. A cable at an angle of 30.0° with the beam
A 15.0-m uniform ladder weighing 500 N rests against a frictionless wall. The ladder makes a 60.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the
A uniform ladder of length L and mass m1 rests against a frictionless wall. The ladder makes an angle) with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base
Figure P12.15 shows a claw hammer as it is being used to pull a nail out of a horizontal board. If a force of 150 N is exerted horizontally as shown, find(a) The force exerted by the hammer claws on
A uniform plank of length 6.00 m and mass 30.0 kg rests horizontally across two horizontal bars of a scaffold. The bars are 4.50 m apart, and 1.50 m of the plank hangs over one side of the scaffold.
A 1 500-kg automobile has a wheel base (the distance between the axles) of 3.00 m. The center of mass of the automobile is on the center line at a point 1.20 m behind the front axle. Find the force
A vertical post with a square cross section is 10.0 m tall. Its bottom end is encased in a base 1.50 m tall, which is precisely square but slightly loose. A force 5.50 N to the right acts on the top
A flexible chain weighing 40.0 N hangs between two hooks located at the same height (Fig. P12.19). At each hook, the tangent to the chain makes an angle θ= 42.0° with the horizontal.
Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed in his quest to improve communication between damsels and dragons (Fig. P12.20). unfortunately his squire lowered the
In the situation described in Problem 20 and illustrated in Figure P12.20, the lift cable suddenly breaks! The hinge between the castle wall and the bridge is frictionless, and the bridge swings
Stephen is pushing his sister Joyce in a wheelbarrow when it is stopped by a brick 8.00 cm high (Fig. P12.22). The handles make an angle of 15.0° below the horizontal. A downward force of 400 N
One end of a uniform 4.00-m-long rod of weight Fg is supported by a cable. The other end rests against the wall, where it is held by friction, as in Figure P12.23. The coefficient of static friction
Two identical uniform bricks of length L are placed in a stack over the edge of a horizontal surface with the maximum overhang possible without falling, as in Figure P12.24. Find the distance x.
A vaulter holds a 29.4-N pole in equilibrium by exerting an upward force U with her leading hand and a downward force D with her trailing hand, as shown in Figure P12.25. Point C is the center of
In the What If? Section of Example 12.3, let x represent the distance in meters between the person and the hinge at the left end of the beam. (a) Show that the cable tension in newtons is given by

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