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mechanics

Questions and Answers of Mechanics

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at
The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A .30-caliber bullet has mass 0.00720 kg and a speed of 601 m/s relative to the muzzle when fired from a rifle that
Block A in Fig. 8.35 has mass 1.00 kg, and block B has mass 3.00 kg. The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level,
A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20-g bullets at 965 m/s. The mass of the hunter (including his gun) is 72.5 kg, and the hunter holds tight to the gun
An atomic nucleus suddenly bursts apart (fissions) into two pieces. Piece A, of mass mA' travels off to the left with speed VA Piece B, of mass mB, travels off to the right with speed VB' (a) Use
The nucleus of 21'PO decays radioactively by emitting an alpha particle (mass 6.65 X 10-27 kg) with kinetic energy 1.23 X 10-12 J, as measured in the laboratory reference frame. Assuming that the Po
You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off 1he ice, you throw 1he rock so it bas velocity 12.0 m/s relative to 1he earth a1 an angle of 35.0
Two ice skaters, Daniel (mass 65.0 kg) and Rebecca (mass 45.0 kg), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 m/s before she
An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is 78.4 kg,
Changing Mass An open-topped freight car with mass 24,000 kg is coasting without friction along a level track. It is raining very hard, and the rain is falling vertically downward. Originally, the
Asteroid Collision Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at 40.0 m/s, is deflected 30.0"
A 15.0-kg fish swimming at 1.10 m/s suddenly gobbles up a 4.50-kg fish that is initially stationary. Neglect any drag effects of the water. (a) Find the speed of the large fish just after it eats
Two fun-loving otters are sliding toward each other on a muddy (and hence Iiictioo1ess) horizontal surface. One of them, of mass 7.so kg, is sliding to the left at 5.00 m/s, while the other, of mass
Deep Impact Mission in July 2005, NASA's "Deep Impact" mission crashed a 372-kg probe directly onto 1he surface of the comet Tempell, hitting the surface at 37,000 km/h. The original speed of the
A 1050-kg sports car is moving westbound a11S.0 m/s on a level road when it collides with a 632O-kg truck driving east on the same road at 10.0 m/s. The two vehicles remain locked together after 1he
On a very muddy football field, a 110-kg linebacker tackles an 85-kg halfback. Immediately before the collision, the linebacker is slipping with a velocity of 8.8 m/s north and the halfback is
Two skaters collide and grab on to each other on flectionless ice. One of them, of mass 70.0 kg, is moving to the right at 200 m/s, while the other, of mass 65.0 kg, is moving to the left at 2.5O
Two cars, one a compact with mass 1200 kg and 1he other a large gas-guzzler with mass 3000 kg, collide head-on at typical freeway speeds. (a) Which car has a greater magnitude of momentum change?
At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling
Bird Defense to protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 6()().g falcon flying at 20.0 m/s hit a l.50-kg
A 5.00-g bullet is fired horizontally into a 1.20-kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet remains embedded
A Ballistic Pendulum a 12.0-g ride bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long (see Example 8.8 in Section 8.3).
You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 80.0 kg, is given a push and slides eastward. Abigail, with mass
Blocks A (mass 2.00 kg) and B (mass 10.00 kg) moves on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 2.00 m/s. The blocks are equipped with
A 0.150-kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 m/s. It has a head-on collision with a 0.300-kg glider that is moving to the left with a speed of
A 10.0-g marble slides to the left with a velocity of magnitude 0.400 m/s on the frictionless, horizontal surface of an icy New York sidewalk and has a head-on, elastic collision with a larger 30.0-g
Supply the details of the calculation of a and B in Example 8.12 (Section 8.4).
Moderator’s Canadian nuclear reactors use heavy Wafer moderators in which elastic collisions occur between the neutrons and deuterons of mass 2.0 u (see Example 8.11 in Section 8.4). (a) What is
You are at the controls of a particle accelerator, sending a beam of 1.50 X 107 m}s protons (mass m) at a gas target of an unknown element. Your detector tells you that some protons bounce straight
Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (I) 0.300 kg, (0.200 m, 0.300m); (2) 0.400 kg, (0.100m, -0.400m); (3) 0.200 kg, (-0.300 m, 0.600 m).
Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets combined, this is essentially the position of the center of
Pluto and Charon Pluto's diameter is approximately 2370 km, and the diameter of its satellite Charon is 1250 kin. Although the distance varies, they are often about 19,700 kin apart,
A 1200-kg station wagon is moving along a straight highway at 12.0 m/s. Another car, with mass 1800 kg and speed 20.0 m/s, has its center of mass 40.0 m ahead of the center of mass of the station
A machine part consists of a thin, uniform 4.00-kg bar that is 1.50 m long, hinged perpendicular to a similar vertical bar of mass 3.00 kg and length 1.80 m. The longer bar has a small but dense
At one instant, the center of mass of a system of two particles is located on the x-axis at x = 2.0 m and has a velocity of (5.0 m/s) One of the particles is at the origin. The other particle has a
In Example 8.14 (Section 8.5), Ramon pulls on the rope to give himself a speed of 0.70 m/s. What is James's speed?
A system consists of two particles. At t = 0 one particle is at the origin; the other, which has a mass of 0.50 kg, is on the y-axis at y = 6.0 m. At t = 0 the center of mass of the system is on the
A radio-controlled model airplane has a momentum given by [( -0.75 kg' m/s')t2 + (3.0 kg' m/s)]i+ (0.25 kg' m/s2 )tj. What are the X-, y-, and z-components of the net force on the airplane?
A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (a) What is the thrust of the rocket? (b) Would the rocket
A 70-kg astronaut floating in space in a 1l0-kg MMU (manned maneuvering unit) experiences an acceleration of 0.029 m/s2 when he fires one of the MMU's thrusters. (a) If the speed of the escaping N2
A rocket is fired in deep space, where gravity is negligible. If the rocket has an initial mass of 6000 kg and ejects gas at a relative velocity of magnitude 2000 m/s, how much gas must it eject in
A rocket is fired in deep space, where gravity is negligible. In the first second it ejects, k of its mass as exhaust gas and has an acceleration of 15.0 m/s2. What is the speed of the exhaust gas
A C6-5 model rocket engine has an impulse of 10.0 Ns for 1.70 s, while burning 0.0125 kg of propellant. It has a maximum thrust of 13.3 N. The initial mass of the engine plus propellant is 0.0258 kg.
A single-stage rocket is fired from rest from a deep-space platform, where gravity is negligible. If the rocket burns its fuel in 50.0 s and the relative speed of the exhaust gas is v~ = 2100 m/s,
Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. (a) If the
A steel ball with mass 40.0 g is dropped from a height of 2.00 m onto a horizontal steel slab. The ball rebounds to a height of 1.60 m. (a) Calculate the impulse delivered to the ball during
In a volcanic eruption, a 24OQ.kg boulder is throw vertically upward into the air. At its highest point, it suddenly explodes (due to trapped gases) into two fragments, one being three times the mass
Just before it is struck by a racket, a tennis ball weighing 0.560 N has a velocity of (20.0 m/s)i - (4.0 m/s )J. During the 3.00 IDS that the racket and ball are in contact, the net force on the
Three coupled railroad cars roll along and couple with a fourth car, which is initially at rest. These four cars roll along and couple with a fifth car initially at rest. This process continues until
A 1500-kg blue convertible is traveling south, and a 200D-kg red SUY is traveling west. If the total momentum of the system consisting of the two cars is 8000 kg m/s directed at 60.0° west of south,
Three identical pucks on a horizontal air table have repelling magnets. They are held together and then released simultaneously. Each has the same speed at any instant. One puck moves due west. What
Spheres A (mass 0.020 kg), B (massO.030kg) and C (mass 0.050 kg) are approaching the origin as they slide on a frictionless air table (Fig. 8.41). The initial velocities of A and B are given in the
A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 200 kg and is
Changing Mass A railroad hopper car filled with sand is rolling with an initial speed of 15.0 m/s on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass
At a classic auto show, a 840-kg 1955 Nash Metropolitan motors by at 9.0 m}s, followed by a 162G-kg 1957 Packard Clipper purring past at 5.0 m/s. (a) Which car has the greater kinetic energy? What
A soldier on a firing range fires an eight-shot burst from an assault weapon at a full automatic rate of 1000 rounds per minute. Each bullet has a mass of 7.45 g and a speed of 293 m/s relative to
A 0.15G-kg frame, when suspended from a coil spring, stretches the spring 0.050 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm (Fig. 8.42). Find the maximum
A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (Fig. 8.43). The impact
A Ricocheting Bullet 0.100-kg stone rests on a frictionless, horizontal surface. A bullet of mass 6.00 g, traveling horizontally at 350 m/s, strikes the stone and rebounds horizontally at right
A movie stuntman (mass 80.0 kg) stands on a window ledge 5.0 m above the floor (Fig. 8.44). Grabbing a rope attached to a chandelier, he swings down to grapple with the movie's villain (mass 70.0
Two identical masses are released from rest in a smooth hemispherical bowl of radius R, from the position shown in Fig. 8.45. You can ignore friction between the masses and the surface of the bowl.
A ball with mass M, moving horizontally at 5.00 m/s, collides elastically with a block with mass 3M that is initially hanging at rest from the ceiling on the end of a 50.G-cm wire. Find the maximum
A 20.00-kg lead sphere is hanging from a hook by a thin wire 3.50 m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00-kg steel dart that embeds itself in
An 8.00-kg ball, hanging from the ceiling by a light wire 135 cm long, is struck in an elastic collision by a 2.00-kg ball moving horizontally at 5.00 m/s just before the collision. Find the tension
A rubber ball of mass m is released from rest at height h above the floor. After its first bounce, it rises to 90% of its original highly what impulse (magnitude and direction) does the floor exert
A 4.00-g bullet, traveling horizontally with a velocity of magnitude 400 m/s, is fired into a wooden block with mass 0.800 kg, initially at rest on a level surface. The bullet passes through the
A 5.00-g bullet is shot through a 1.00-kg wood block suspended on a string 2.00 m long. The center of mass of the block rises a distance of 0.45 cm. Rod the speed of the bullet as it emerges from the
A neutron with mass m makes a head-on, elastic collision with a nucleus of mass M, which is initially at rest. (a) Show that if the neutron's initial kinetic energy is K, the kinetic energy that it
Energy Sharing in Elastic Collisions a stationary object with mass mB is struck head-on by an object with mass mA that is moving initially at speed Vo. (a) If the collision is elastic, what
In a shipping company distribution center, an open cart of mass 50.0 kg is rolling to the left ataspeedof5.00m/s(Fig.8.46). You can ignore friction between the cart and the floor. A 15.0-kg package
A blue puck with mass 0.0400 kg sliding with a velocity of magnitude 0.200 m/. on a frictionless, horizontal air table, makes a perfectly elastic, head-on collision with a red puck with mass m,
Two asteroids with masses mA and mB are moving with velocities VA and VB with respect to an astronomer in a space vehicle.(a) Show that the total kinetic energy as measured by the astronomer is with
Suppose you hold a small ball in contact with, and directly over, the center of a large ball. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with
Jack and Jill are standing on Ii crate at rest on the frictionless horizontal surface of a frozen pond. Jack has mass 15.0 kg, Jill has mass 45.0 kg, and the crate has mass 15.0 kg. They remember
Energy Sharing an object with mass in initially at rest, explodes into two fragments, one with mass mA and the other with mass mB' where mA + mB = m. (a) If energy Q is released in the explosion,
Neutron Decay a neutron at rest decays (breaks up) to a proton and an electron. Energy is released in the decay and appears as kinetic energy of the proton and electron. The mass of a proton is 1836
A 23'Tb (thorium) nucleus at rest decays to a 228Ra (radium) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 X 10-13 J. An alpha particle has
Antineutrino in beta decay, a nucleus emits an electron. A 210Bi (bismuth) nucleus at rest undergoes beta decay to 210PO (Polonium). Suppose the emitted electron moves to the right with a momentum of
A proton moving with speed VAl in the +x-direction makes an elastic, off-enter collision with an identical proton originally at rest. After impact, the first proton moves with speed V A2 in the first
Hockey puck B rests on a smooth ice surface and is struck by a second puck A, which has the same mass. Puck A is initially traveling at 15.0 m/s and is deflected 25.00 from its initial direction.
Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan's weight is 800 N, Jane's weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the
The objects in Fig. 8.47 are constructed of uniform wire bent into the shapes shown. Find the position of the center of mass of each.
A 45.O-kg woman stands up in a 60.O-kg canoe 5.00 m long. She walks from a point 1.00 m from one end to a point 1.00 m from the other end (Fig. 8.48). If you ignore resistance to motion of the canoe
You are standing on a concrete slab that in torn is resting on a frozen lake. Assume there is no friction between the slab and the ice. The slab has a weight five times your weight. If you begin
A 20.O-kg projectile is fired at an angle of 60.0 above the horizontal with a speed of 80.0 m/s. At the highest point of its trajectory, Ibe projectile explodes into two fragments with equal mass,
A fireworks rocket is fired vertically upward. At its maximum height of 80.0 m, it explodes and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion, 860 J
A 12.0-kg shell is launched at an angle of 55.0 above the horizontal with an initial speed of ISO m/s. When it is at its highest point the shell exploded into two fragments, one three times heavier
A Nuclear Reaction Fission, the process that supplies energy in nuclear power plants, occurs when a heavy nucleus is split into two medium-sized nuclei. One such reaction occurs when a neutron
Center of-Mass Coordinate System Puck A (mass m Al is moving on a frictionless, horizontal air table in the + x-direction with velocity it AI and makes an elastic, head-on collision with puck B (mass
The coefficient of restitution a for a head-on collision is defined as the ratio of the relative speed after the collision to the relative speed before. (a) What is for a completely inelastic
Binding Energy of the Hydrogen Molecule when two hydrogen atoms of mass m combine to form a diatomic hydrogen molecule (H2), the potential energy of the system after they combine is -fl., where fl.
A wagon with two boxes of gold, having total mass 300 kg, is cut loose from the horses by an outlaw when the wagon is at rest 50 m up a 6.00 slope (Fig. 8.50). The outlaw plans to have the wagon roll
In Section 8.6, we considered a rocket fired in outer space where there is no air resistance and where gravity is negligible. Suppose instead that the rocket is accelerating vertically upward from
A Multistage Rocket Suppose the first stage of a two stage rocket has total mass 12,000 kg, of which 9000 kg is fuel. The total mass of the second stage is 1000 kg, of which 700 kg is fuel. Assume
For the rocket described in Examples 8.15 and 8.16 (Section 8.6), the mass of the rocket as a function of time is (a) Calculate and graph the velocity of the rocket as a function of time from t = 0
In Section 8.5 we calculated the center of mass by considering objects composed of ajinite number of point masses or objects that, by symmetry, could be represented by a finite number of point
Use the methods of Challenge Problem 8.113 to calculate the x- and y-coordinates of the center of mass of a semicircular metal plate with uniform density p and thickness t. Let the radius of the
One-fourth of a rope of length l is banging down over the edge of a frictionless table the rope bas a uniform, linear density (mass per unit length) A (Greek lambda), and the end already on the table
A Variable-Mass Raindrop in a rocket-propulsion problem the mass is variable. Another such problem is a raindrop falling through a cloud of small water droplets. Some of these small droplets adhere
(a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m? What is this angle in degrees? (b) An arc 14.0 cm long on the circumference of a

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