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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

What is the angular momentum vector of the 2.0 kg, 4.0-cm-diameter rotating disk in FIGURE EX12.43? y 600 rpm х FIGURE EX12.43
What are the magnitude and direction of the angular momentum relative to the origin of the 200 g particle in FIGURE EX12.42? 200 g 45° 2.0 m- 3.0 m/s -х 1.0 m
A 1.3 kg ball on the end of a lightweight rod is located at (x, y) = (3.0 m, 2.0 m), where the y-axis is vertical. The other end of the rod is attached to a pivot at (x, y) = (0 m, 3.0 m).What is the
Force F = -10ĵ N is exerted on a particle at r = (5î + 5ĵ) m.What is the torque on the particle about the origin?
Vector A = 3î + ĵ and vector B = 3î - 2ĵ + 2k̂. What is the cross product A × B?
Evaluate the cross products A Ã— B and C Ã— D. (a) AÅ (b) Б 4 90° 45° FIGURE EX12.38
Evaluate the cross products A Ã— B and C Ã— D. (b) (a) A 45°/ FIGURE EX12.37
A solid sphere of radius R is placed at a height of 30 cm on a 15° slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released
An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25° incline. It rolls, without slipping, to the bottom.a. What is the sphere’s angular velocity at the
A 500 g, 8.0-cm-diameter can is filled with uniform, dense food. It rolls across the floor at 1.0 m/s. What is the can’s kinetic energy?
A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s.a. What is the tire’s angular velocity, in rpm?b. What is the speed of a point at the top edge of the tire?c. What is the
A 5.0 kg cat and a 2.0 kg bowl of tuna fish are at opposite ends of the 4.0-m-long seesaw of Figure EX12.32. How far to the left of the pivot must a 4.0 kg cat stand to keep the seesaw balanced? 2.0
The 3.0-m-long, 100 kg rigid beam of Figure EX12.31 is supported at each end. An 80 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam? 2.0 m 3.0 m
The object shown in Figure EX12.30 is in equilibrium. What are the magnitudes of F1and F2? 2.0 m 1.0 m f40 N Massless FIGURE EX12.30
The two objects in Figure EX12.29 are balanced on the pivot.What is distance d? 2.0 m 1.0 m 4.0 kg- 1.0 kg FIGURE EX12.29
A 4.0 kg, 36-cm-diameter metal disk, initially at rest, can rotate on an axle along its axis. A steady 5.0 N tangential force is applied to the edge of the disk. What is the disk’s angular
Starting from rest, a 12-cm-diameter compact disk takes 3.0 s to reach its operating angular velocity of 2000 rpm. Assume that the angular acceleration is constant. The disk’s moment of inertia is
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What net torque will bring the balls to a halt in 5.0 s?
An object whose moment of inertia is 4.0 kg m2experiences the torque shown in Figure EX12.25. What is the object€™s angular velocity at t = 3.0 s? Assume it starts from rest. т (Nm) 0+ -t
An object’s moment of inertia is 2.0 kg m2. Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?
An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 3.8 kg, with the center of mass at 40% of the arm length. What is the magnitude of the torque
A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end
The axle in Figure EX12.21 is half the distance from the center to the rim. What is the net torque about the axle? 5.0 kg 30 cm 15 kg |10 kg FIGURE EX12.21
The 20-cm-diameter disk in Figure EX12.20 can rotate on an axle through its center. What is the net torque about the axle? y 30 N, 30 N 45 5.0 5.0 cт cm 20 N 20 N FIGURE EX12.20
In Figure EX12.19, what magnitude force provides 5.0 N m net torque about the axle? 10 cm 10 cm
In Figure EX12.18, what is the net torque about the axle? 30 N 4.0 cm 20 N
A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door’s moment of inertia for(a) Rotation on its hinges(b) Rotation about a vertical axis inside the door, 15 cm from one edge?
A 12-cm-diameter CD has a mass of 21 g. What is the CD’s moment of inertia for rotation about a perpendicular axis(a) Through its center(b) Through the edge of the disk?
The three masses shown in Figure EX12.15 are connected by massless, rigid rods.a. Find the coordinates of the center of mass.b. Find the moment of inertia about an axis that passes through mass A and
The four masses shown in Figure EX12.13 are connected by massless, rigid rods.a. Find the coordinates of the center of mass.b. Find the moment of inertia about a diagonal axis that passes through
Is the angular momentum of disk a in FIGURE Q12.13 larger than, smaller than, or equal to the angular momentum of disk b? Explain. Ib = 2r, т т wn = 2w, b FIGURE Q12.13
The four masses shown in Figure EX12.13 are connected by massless, rigid rods.a. Find the coordinates of the center of mass.b. Find the moment of inertia about an axis that passes through mass A and
A diver in the pike position (legs straight, hands on ankles) usually makes only one or one-and-a-half rotations. To make two or three rotations, the diver goes into a tuck position (knees bent, body
A drum major twirls a 96-cm-long, 400 g baton about its center of mass at 100 rpm. What is the baton’s rotational kinetic energy?
The solid cylinder and cylindrical shell in FIGURE Q12.11 have the same mass, same radius, and turn on frictionless, horizontal axles.(The cylindrical shell has lightweight spokes connecting the
The three 200 g masses in Figure EX12.11 are connected by massless, rigid rods.a. What is the triangle€™s moment of inertia about the axis through the center?b. What is the
What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.
A student gives a quick push to a ball at the end of a massless, rigid rod, as shown in FIGURE Q12.9, causing the ball to rotate clockwise in a horizontal circle. The rod€™s pivot is
A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?
Six forces are applied to the door in FIGURE Q12.8. Rank in order, from largest to smallest, the six torques Ï„ato Ï„fabout the hinge on the left. Explain. таF LI4 L/4 L/4 L/4
A 100 g ball and a 200 g ball are connected by a 30-cm-long, massless, rigid rod. The balls rotate about their center of mass at 120 rpm. What is the speed of the 100 g ball?
The professor hands you two spheres. They have the same mass, the same radius, and the same exterior surface. The professor claims that one is a solid sphere and the other is hollow. Can you
The three masses shown in Figure EX12.7 are connected by massless, rigid rods. What are the coordinates of the center of mass? B 300 g 10 cm 12 cm х 100 g 200 g FIGURE EX12.7
You have two solid steel spheres. Sphere 2 has twice the radius of sphere 1. By what factor does the moment of inertia I2 of sphere 2 exceed the moment of inertia I1 of sphere 1?
The three masses shown in Figure EX12.6 are connected by massless, rigid rods. What are the coordinates of the center of mass? 200 g B 10 cm 10 cm A 100 g 300 g FIGURE EX12.6
The moment of inertia of a uniform rod about an axis through its center is 1/12 mL2. The moment of inertia about an axis at one end is 1/3 mL2. Explain why the moment of inertia is larger about the
How far from the center of the earth is the center of mass of the earth + moon system? Data for the earth and moon can be found inside the back cover of the book.
Must an object be rotating to have a moment of inertia? Explain.
An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling
A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off.a. What is the speed of the tip of a blade 10 s after the fan is turned
FIGURE Q12.3 shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies Kato Kc. 2w 2r FIGURE Q12.3 len
A skater holds her arms outstretched as she spins at 180 rpm. What is the speed of her hands if they are 140 cm apart?
If the angular velocity Ï‰ is held constant, by what factor must R change to double the rotational kinetic energy of the dumbbell in FIGURE Q12.2? т, R M2 FIGURE Q12.2
A high-speed drill reaches 2000 rpm in 0.50 s.a. What is the drill’s angular acceleration?b. Through how many revolutions does it turn during this first 0.50 s?
Is the center of mass of the dumbbell in FIGURE Q12.1 at point a, b, or c? Explain. a b FIGURE Q12.1
Section 11.6 found an equation for vmax of a rocket fired in deep space. What is vmax for a rocket fired vertically from the surface of an airless planet with free-fall acceleration g? Referring to
The air-track carts in FIGURE CP11.83 are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 120 N/m and is compressed 4.0 cm. The carts slide past a flame that burns
A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. Explosive bolts release the first stage and push it backward with a speed of 35 m/s
A 20 kg wood ball hangs from a 2.0-m-long wire. The maximum tension the wire can withstand without breaking is 400 N.A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood
A spaceship of mass 2.0 × 106 kg is cruising at a speed of 5.0 × 106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 × 105 kg, is blown
A 1000 kg cart is rolling to the right at 5.0 m/s. A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of
You are given the equation(s) used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problem,
a. To understand why rockets often have multiple stages, first consider a single-stage rocket with an empty mass of 200 kg, 800 kg of fuel, and a 2000 m/s exhaust speed.If fired in deep space, what
A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rocket’s speed 10 s,
A 2100 kg truck is traveling east through an intersection at 2.0 m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling
FIGURE P11.71 shows a collision between three balls of clay.The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay? 40 g JASO 45° 4.0 m/s 3.0
A 20 g ball of clay traveling east at 2.0 m/s collides with a 30 g ball of clay traveling 30° south of west at 1.0 m/s. What are the speed and direction of the resulting 50 g blob of clay?
A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic
The nucleus of the polonium isotope 214Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleus with mass 4 u). Laboratory experiments measure the speed of the alpha
A proton (mass 1 u) is shot toward an unknown target nucleus at a speed of 2.50 × 106 m/s. The proton rebounds with its speed reduced by 25% while the target nucleus acquires a speed of 3.12 × 105
Old naval ships fired 10 kg cannon balls from a 200 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship.
A 100 g ball moving to the right at 4.0 m/s collides head-on with a 200 g ball that is moving to the left at 3.0 m/s.a. If the collision is perfectly elastic, what are the speed and direction of each
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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°
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
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
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
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
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
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
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
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
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,
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
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

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