PHY II EXAM 2
A system of 3 masses is located as follows: m1 = m0 at (0, L), m2 = 2m0 at the origin, and m3 = 3m0 at (3L, 0). Where is the center of mass of these masses?
(3/2L,1/6L)
Two billiard balls have velocities of 4.0 m/s and -1.0 m/s when they meet in an elastic head-on collision. What is the final velocity of the first ball after collision?
-1.0 m/s
A hill is 150 m long and makes an angle of 12° with the horizontal. As a 60-kg jogger runs up the hill, how much work does gravity do on the jogger?
-1.83 E +4 J
A 22.3-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s. What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?
-10.8 kJ
A ball with original momentum +7.0 kg⋅m/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is:
-14 kg*m/s
A 3.00-kg ball has zero potential and kinetic energy. Maria drops the ball into a 10.0-m-deep well. After the ball comes to a stop in the mud, the sum of its potential and kinetic energy is:
-294 J
Two identical 7-kg bowling balls roll toward each other. The one on the left is moving at +4 m/s while the one on the right is moving at −4 m/s. What is the velocity of each ball after they collide elastically?
-4 m/s, +4 m/s
A horse pulls a 350-kg sled at constant speed along an icy road for a distance of 500 m. If the coefficient of kinetic friction between the sled and the road is 0.450, and the angle between the harness and the sled is 25°, what is the mechanical energy lost due to friction?
-6.4E +5 J
A "double satellite" is launched into space. It consists of a satellite of mass m and another satellite of mass 5m. The connecting mechanism of these satellites is an explosive bolt and a compressed spring, both of negligible mass. The bolt is exploded and the satellites drift apart having been pushed by the spring. When the less massive satellite has moved a distance of 2.5 m from the center of mass of the double satellite, how far away from it is the satellite of greater mass?
...
A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s2 over a 5.0-s interval. What is the tangential component of acceleration for a point on the outer edge of the tire during the 5.0-s interval?
...
A 0.650-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. If the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?
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A 5.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, −4.0) m. What is the moment of inertia of this system of masses about the x axis?
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A bucket of water with total mass 26 kg is attached to a rope, which in turn is wound around a 0.04-m radius cylinder at the top of a well. A crank with a turning radius of 0.20 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.11 kg·m2. If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)
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A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.70 m long and each ball on the end is 0.10 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?
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A roller coaster, loaded with passengers, has a mass of 2 000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? (g = 9.8 m/s2)
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A rotating flywheel can be used as a method to store energy. If it has 2.00 × 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.00 Nm acts on the system, in what interval of time would the flywheel come to rest?
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A satellite is in a circular orbit about the Earth at a distance of two Earth radii above the surface. What is the speed of the satellite? (The radius of the Earth is 6.4 × 106 m, and G = 6.67 × 10−11 N × m2/kg2.)
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A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15°, and rolls to the bottom without slipping. (For a cylinder I = MR2.) The upper end of the ramp is 1.5 m higher than the lower end. Find the linear speed of the cylinder when it reaches the bottom of the ramp. (g = 9.8 m/s2)
...
A turntable has a moment of inertia of 3.00 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?
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A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark. What is the weight of the meterstick?
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A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units). If the speed of the helium nucleus is 5.5 × 105 m/s, what is the speed of the thorium nucleus?
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A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing?
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An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s2?
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An object weighs 300 N. If the gravitational constant G were half of what it is currently, what would the weight of the object be?
...
Neglecting gravity, doubling the exhaust velocity from a single stage rocket initially at rest changes the final kinetic energy of the burnout stage by what factor? Assume all other variables, such as the mass of the rocket and the mass of the fuel, do not change.
...
Two satellites are monitored as they orbit the Earth; satellite X is eight times as far from the Earth's center as is satellite Y. From Kepler's third law one may conclude that the period or revolution of X is what factor times that of Y?
...
A cylindrical space colony 8.00 km in diameter and 30.0 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land, and lakes on the inside surface and air and clouds in the center. All this would be held in place by the rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder?
0.049 rad/s
Two skaters, both of mass 75.0 kg, are on skates on a frictionless ice pond. One skater throws a 0.40-kg ball at 6.0 m/s to his friend, who catches it and throws it back at 6.0 m/s. When the first skater has caught the returned ball, what is the velocity of each of the two skaters?
0.063 m/s, moving apart
A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s2)
0.28
A Ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration?
0.37 rad/s2
I drop a 55-g golf ball from 2.50 m high. It rebounds to 1.65 m. How much energy is lost?
0.46 J
Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?
0.50 T
A ventilation fan has blades 0.25 m in radius rotating at 20 rpm. What is the tangential speed of each blade tip?
0.52 m/s
An object with mass m and moment of inertia I is spinning with an angular momentum L. Its kinetic energy is:
0.5L2/l
A Ferris wheel, rotating initially at an angular speed of 0.50 rad/s, accelerates over a 7.0-s interval at a rate of 0.040 rad/s2. What is its angular speed after this 7.0-s interval?
0.78 rad/s
A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.250 m/s?
0.80 rev/s
A 75.0-kg swimmer dives horizontally off a 465-kg raft initially at rest. If the diver's speed immediately after leaving the raft is 5.00 m/s, what is the corresponding raft speed?
0.806 m/s
A turntable has a moment of inertia of 3.0 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25 rev/min. A 0.60-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center. By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?
0.83
Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?
0.94 m
A ventilation fan with a moment of inertia of 0.034 kg·m2 has a net torque of 0.11 N·m applied to it. If it starts from rest, what angular momentum will it have 9.0 s later?
0.99 kg·m2/s
A turntable has a moment of inertia of 3.00 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center. By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?
1.00 - no change
Anika and Sam are astronauts floating in space outside their spaceship. They are tethered together by a rope of length 10.5 m. They both begin pulling on the rope at the same time. Anika has mass of 80 kg, and Sam 100 kg. Because her mass is less, Anika reaches the middle of the rope first. Assuming the center of the rope is at the origin and that Anika and Sam start at 5.25 m and -5.25 m, respectively, where is Sam when Anika reaches the middle?
1.05 m
A 1 500-kg experimental rocket sled at rest on level frictionless rails is loaded with 55.0 kg of propellant. It exhausts the propellant in a 20-s "burn." The rocket moves at 155 m/s after the burn. What average force is experienced by the rocket during the burn?
1.16E +4 N
A 2 500-kg ore car rolls 55.0 m down a frictionless 10.0° incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the ore car in a distance of 2.10 m?
1.1E + 5 kN/m
A bucket of water with total mass 21.0 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.21 kgm2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 5.4 m/s?
1.2E+3 J
A 180-hp engine can deliver, in SI units, an average power of ____. (1 hp = 746 W)
1.3 E + 5 W
A cannon of mass 1 300 kg fires a 13.6-kg shell with a velocity of 180 m/s at an angle of 45° above the horizontal. Find the recoil velocity of the cannon across the level ground.
1.33 m/s
A 13.4-g bullet is fired into a 1.60-kg block of wood which is suspended as a ballistic pendulum. The combined mass swings up to a height of 8.50 cm. What was the kinetic energy of the combined mass immediately after the collision?
1.34 J
A 5.00-g bullet is fired into a 950-g block of wood suspended as a ballistic pendulum. The combined mass swings up to a height of 8.00 cm. What was the kinetic energy of the bullet immediately before the collision?
1.4E + 2 J
A 6.1-g bullet has a velocity of 475 m/s when it penetrates a wooden door to a depth of 3.5 cm. Assuming the frictional force that stops the bullet is constant, how long does it take from the time the bullet hits the door till it comes to a stop?
1.5E -4 s
A 60-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 25 kg and it makes an angle of 60° with the ground, find the force of friction of the ground on the foot of the ladder.
1.6E + 2 N
An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 2.0 N. What is the object's mass? (g at the surface of the Earth is 9.80 m/s2)
1.8 kg
For any object orbiting the Sun, Kepler's law may be written T2 = kr3. If T is measured in years and r in units of the Earth's distance from the Sun, then k = 1. What, therefore, is the time (in years) for Mars to orbit the Sun if its mean radius from the Sun is 1.5 times the Earth's distance from the Sun?
1.8 yrs
A 0.10-kg ball is moving at 7.0 m/s when it is hit by a bat, causing it to reverse direction and have a speed of 12.0 m/s. What is the change in the magnitude of the momentum of the ball?
1.9 kg*m/s
A hoop with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy? (For a hoop, I = MR2.)
1/1
A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by KE = Mv2 when rolling down an incline. What is this object's moment of inertia?
1/5 MR2
A boat with mass of 1 200 kg is traveling at 12 m/s. What is the magnitude of the force required to stop the boat if it undergoes a displacement of 85 m?
1000 N
Petra pushes a crate across a rough floor. A frictional force of 28.0 N acts to oppose the motion of the crate, and Petra pushes with a horizontal force of 36.4 N. If the net work Petra does is 94.5 J, through what distance did she push the crate?
11.3
A miniature spring-loaded, radio-controlled gun is mounted on an air puck. The gun's bullet has a mass of 7.00 g, and the gun and puck have a combined mass of 150 g. With the system initially at rest, the radio controlled trigger releases the bullet causing the puck and empty gun to move with a speed of 0.530 m/s. What is the bullet's speed?
11.4 m/s
An amount of work equal to 2.0 J is required to compress the spring in a spring-gun. What is the "launch speed" of a 26.0-g marble?
12.4 m/s
A 24.0-kg crate, initially at rest, slides down a ramp 4.0 m long and inclined at an angle of 20° with the horizontal. If there is no friction between ramp surface and crate, what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s2)
322 J
A girl and her bicycle have a total mass of 42 kg. At the top of the hill her speed is 4.00 m/s. The hill is 14.3 m high and 112 m long. If the force of friction as she rides down the hill is 20 N, what is her speed at the bottom?
13.8 m/s
Popeye, of mass 75.0 kg, has just downed a can of spinach. He accelerates quickly and stops Bluto, of mass 650 kg (Bluto is very dense), who is charging in at 15.0 m/s. What was Popeye's speed?
130 m/s
A 0.150-m-radius grinding wheel, starting at rest, develops an angular speed of 12.0 rad/s in a time interval of 4.00 s. What is the centripetal acceleration of a point 0.100 m from the center when the wheel is moving at an angular speed of 12.0 rad/s?
14.4 m/s2
At what angle (relative to the horizontal) should a curve 52.0 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 11.6 m/s? (g = 9.80 m/s2)
14.8 degrees
A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 250 kg and radius 0.500 m (Icylinder = MR2/2). If the bus requires an average power of 10.0 kW, how long will the flywheel rotate?
154 s
A baseball outfielder throws a baseball of mass 0.36 kg at a speed of 34.0 m/s and initial angle of 30°. What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction.
156 J
A Hooke's law spring is compressed 14.6 cm from equilibrium, and the potential energy stored is 76.0 J. What compression (as measured from equilibrium) would result in 100 J being stored in this case?
16.7 cm
A soccer ball (mass = 0.43 kg) is moving at a speed of 20 m/s when it is kicked with a force of 300 N resulting in it going in the opposite direction with the same speed as before. What is the magnitude of the impulse delivered to the ball?
17 kg*m/s
A 70-kg swimmer dives horizontally off a 500-kg raft. The diver's speed immediately after leaving the raft is 6.0 m/s. A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface. If the time interval is read as 0.25 s, what is the magnitude of the average horizontal force by diver on the raft?
1700 N
Rupel pushes a box 7.00 m by applying a 25.0-N horizontal force. What work does she do?
175 J
A baseball pitcher, loosening up his arm before a game, tosses a 0.140-kg ball using only the rotation of his forearm, 0.290 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.450 s, what is the average angular acceleration of the arm and ball?
184 rad/s2
A ventilation fan with a moment of inertia of 0.0340 kg·m2 has a net torque of 0.110 Nm applied to it. If it starts from rest, what kinetic energy will it have 10.4 s later?
19.2 J
An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the Sun. What is its linear speed when it is at its greatest distance from the Sun, a distance 2d?
2 km/s
An initially installed flywheel can store 106 J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a stronger material. If its mass is the same as that of the original, and it is now capable of achieving a rotational speed of 425 rad/s, what maximum energy can be stored?
2.01E+6 J
A baseball pitcher loosens up his pitching arm. He tosses a 0.140-kg ball using only the rotation of his forearm, 0.270 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.425 s, what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?
2.13 N*m
Yuri, a Russian weightlifter, is able to lift 260 kg 2.10 m in 2.20 s. What is his power output?
2.43 kW
The escape speed from the surface of the Earth is 11.2 km/s. Estimate the escape speed for a spacecraft from the surface of the Moon. The Moon has a mass 1/81 that of Earth and a radius 0.25 that of Earth.
2.5 km/s
A 100-W light bulb is left on for 8.0 hours. Over this period of time, how much energy was used by the bulb?
2.9E +6 J
At what speed will a car round a 52.0-m-radius curve, banked at a 40.0° angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.80 m/s2)
20.7 m/s
What centripetal force does an 80.0-kg passenger experience when seated 10.0 m from the center of a Ferris wheel whose angular speed is 0.500 rad/s?
200 N
A bucket of water with total mass 20.0 kg is attached to a rope, which in turn is wound around a 4.00-cm radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.00 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?
200 rad/s
Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 36.0 seconds have elapsed. How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 36.0-second interval?
22.2 s
Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 60.0° N latitude. The radius of the Earth is 6.40 × 106 m.
233 m/s
An automobile accelerates from zero to 36.72 m/s in 6.80 s. The wheels have a diameter of 0.450 m. What is the average angular acceleration of each wheel?
24.0 rad/s2
A uniform, horizontal beam of length 8.0 m and weight 42.4 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60.0° with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium?
24.5 N
A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 5.0-s interval?
25 rad
The end of the cutting cord on a gas-powered weed cutter is 0.21 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?
26 m/s
Jerome pitches a baseball of mass 0.300 kg. The ball arrives at home plate with a speed of 40.0 m/s and is batted straight back to Jerome with a return speed of 52.0 m/s. What is the magnitude of change in the ball's momentum?
27.6 kg*m/s
2 600 rev/min is equivalent to which of the following?
272 rad/s
Old Faithful geyser in Yellowstone Park shoots water hourly to a height of 40.0 m. With what velocity does the water leave the ground?
28.0 m/s
A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum speed can the mass have if the string is not to break?
29 m/s
Mitch throws a 130-g lump of clay at a 590-g target, which is at rest on a horizontal surface. After impact, the target, including the attached clay, slides 2.8 m before stopping. If the coefficient of friction is μ = 0.50, find the speed of the clay before impact.
29 m/s
A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°. It rolls to the bottom without slipping. The upper end of the ramp is 1.20 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.
29.4 J
If a planet has 3 times the radius of the Earth, but has the same density as the Earth, what is the gravitational acceleration at the surface of the planet? (g = 9.80 m/s2)
29.4 m/s2
The distance from the center of a Ferris wheel to a passenger seat is 12 m. What centripetal acceleration does a passenger experience when the wheel's angular speed is 0.50 rad/s?
3.0 m/s2
A disk has a moment of inertia of 3.0 × 10−4 kg·m2 and rotates with an angular speed of 3.6 rad/s. What net torque must be applied to bring it to rest within 3.6 s?
3.00E-4 N·m
A horizontal force of 85.0 N is applied to move a 46.0-kg cart across a 4.0-m level surface. What work is done by the 85.0-N force?
3.4E + 2 J
A 26.0-g bullet moving at 1 200 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?
3.4E +2 J
A 10.0-kg box starts at rest and slides 3.90 m down a ramp inclined at an angle of 10° with the horizontal. If there is no friction between the ramp surface and crate, what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)
3.64 m/s
The Earth is 93.0 million miles from the Sun and its period of revolution is 1 year = 3.15 × 107 s. What is the acceleration of the Earth in its orbit about the Sun?
3.70 × 10−6 mi/s2
Ann the Astronaut weighs 65.0 kg. She is space walking outside the space shuttle and pushes a 350.0-kg satellite away from the shuttle at 0.70 m/s. What speed does this give Ann as she moves toward the shuttle?
3.8 m/s
A 3.00-kg mass is placed at (2.00, 3.00) m, and a 4.50-kg mass is placed at (2.00, −3.00) m. What is the moment of inertia of this system of masses about the y axis?
30.0 kg·m2
A rocket has an exhaust speed of 2.5 × 103 m/s, and produces 7.5 × 105 N of instantaneous thrust. What mass of fuel does the rocket burn each second?
300 kg/s
Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?
all of the above
The law of conservation of momentum is applicable to systems made up of objects described by which of the following?
all of the above answers are valid
Three satellites are launched into space connected together. Once in deep space, an explosive charge separates the three satellites and they move apart. The satellites each have different masses with m1 < m2 < m3. Which of the following statements is always true?
although one or more of the above statements could be true in special cases, they are not always true
In order for a satellite to be geosynchronous, its orbit must:
be over the equator
A billiard ball collides in an elastic head-on collision with a second stationary identical ball. After the collision which of the following conditions applies to the first ball?
comes to rest
A solid sphere and a solid cylinder both have the same radius and mass. If the sphere is spun about an axis through it center with angular velocity sphere, what angular velocity must the cylinder have to the same rotational kinetic energy as the sphere? Round your answer to 2 significant figures.
cylinder = 0.89sphere
As an object is lowered into a deep hole in the surface of the Earth, which of the following must be assumed in regard to its potential energy?
decrease
Which of the following is an example of a nonconservative force?
friction
At an altitude of 5 times the radius of the Earth, the acceleration due to gravity is
g/25
Which of the following best describes the property of the period of orbital revolution for an Earth satellite?
greater when the orbital radius is larger
A 5-kg object is moving to the right at 4 m/s and collides with another object moving to the left at 5 m/s. The objects collide and stick together. After the collision, the combined object:
has less kinetic energy than the system had before the collision
A force of 5.0 N is applied to a 20-kg mass on a horizontal frictionless surface. As the speed of the mass increases at a constant acceleration, the power delivered to it by the force:
increases
An object consists of a rod (of length 3.00 m and negligible moment of inertia) to which four small 3.50-kg masses are attached, one at each end and one at each point on the rod spaced at 1.00-m intervals. The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:
is 49 kg*m2
When a Hooke's law spring is stretched a distance 3x, how much is the increase in energy stored in it from when it was stretched a distance x? Give your answer in terms of a multiple of the energy stored in the spring when it is stretched a distance x.
it is 9x as much
A car is going around a racetrack at constant speed. The curves around the track have different radii. In which turn is the magnitude of the car's acceleration the greatest?
it is the greatest in the turn with the smallest radius
A spring with spring constant k is used to launch a mass m up a frictionless inclined plane having angle of elevation θ. What is the maximum height reached above the starting elevation of the mass during the motion of the mass if the spring is compressed a distance d before launch?
kd^2/2mg
The units of impulse are equivalent to:
kg*m/s
The SI units for k, the spring constant, are equivalent to:
kg/s^2
In a two-body collision, if the momentum of the system is conserved, then which of the following best describes the kinetic energy after the collision?
may also be conserved
A pendulum consists of a mass m suspended from a string of length L. When the pendulum is swinging, how much greater is the mass's potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
mgL (1-costheta)
In a two-body collision, if the kinetic energy of the system is conserved, then which of the following best describes the momentum after the collision?
must also be conserved
At what location does an artificial Earth satellite in elliptical orbit have its greatest speed?
nearest the earth
If the momentum of an object is tripled, its kinetic energy will change by what factor?
nine
Two particles collide, one of them initially being at rest. Is it possible for both particles to be at rest after the collision?
no
Consider a child who is swinging. As she reaches the lowest point in her swing:
none of the above
A high-diver of mass 59.8 kg jumps off a board 10.0 m above the water. If, 1.00 s after entering the water his downward motion is stopped, what average upward force did the water exert?
none of the other answers is correct
According to Kepler's second law, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is at the other focus of the ellipse?
nothing
Object 1 has twice the mass of Object 2. Both objects have the same kinetic energy. Which of the following statements is true?
object 1 has a momentum of greater magnitude than object 2
A model rocket sits on the launch pad until its fuel is ignited, blasting the rocket upward. During the short time of blast-off, as the ignited fuel goes down, the rocket goes up because:
of none of the above reasons
A suitcase is sitting on a horizontal conveyor belt, which is moving at speed v. The work done by the frictional force on the suitcase is
positive
Which of the following is not true about potential energy?
potential energy has direction
The rate at which work is done is equivalent to which of the following?
power
Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?
rad/s2, deg/hour
A rod system with a uniform linear density of l = 4.40 kg/m has the shape shown in the figure, with rod 1 the vertical rod and rod 2 the horizontal rod. Rod 1 has length L1 = 8.00 m, and rod 2 has length L2 = 7.50 m. Neglect the diameter of the rods.
rod 1: 35.2 kg, rod 2: 33.0 kg
A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?
the ball experiences a greater change in momentum than the clay
A block is projected with speed v across a horizontal surface and slides to a stop due to friction. The same block is then projected with the same speed v up an incline where is slides to a stop due to friction. In which case did the total mechanical energy of the block decrease the least?
the case on the inclined surface had the least decrease in total mechanical energy
Neglecting gravity, doubling the exhaust velocity from a single stage rocket initially at rest changes the final velocity attainable by what factor? Assume all other variables, such as the mass of the rocket and the mass of the fuel, do not change.
the final velocity doubles
A hoop, a solid sphere, and a solid cylinder each have the same mass, radius, and initial speed and are going up the same inclined plane. Which one goes the farthest?
the hoop
A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest angular momentum?
the hoop
A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest rotational kinetic energy?
the hoop
An object of mass m moving at speed v0 strikes an object of mass 2m which had been at rest. The first object bounces backward along its initial path at speed v0. Is this collision elastic, and if not, what is the change in kinetic energy of the system?
the kinetic energy increases by mv2
A rock is moving with speed v. If the mass of the rock were tripled and the speed were reduced to v/3, which of the following statements would be true?
the kinetic energy of the rock is smaller than in the first case, but the momenta of both are the same
Two objects, one less massive than the other, collide elastically and bounce back after the collision. If the two originally had velocities that were equal in size but opposite in direction, then which one will be moving faster after the collision?
the less massive one
A 75-kg man is standing in a 20-kg boat. The man steps to the right thinking he is stepping out onto the dock. However, the following will actually happen (ignore the friction of the water or air on the boat or the man):
the man only moves a short distance to the right while the boat moves a larger distance to the left
A tennis ball is held above and in contact with a basketball, and then both are simultaneously dropped. The tennis ball bounces off the basketball at a fairly high speed. This is because:
the massive basketball transfers momentum to the lighter tennis ball
In a partially elastic collision between two objects with unequal mass:
the momentum of one will increase by the amount that the momentum of the other decreases
In order to train for a high-g environment, an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed. In this situation, in which direction is the net force on the astronaut?
the net force is horizontal toward the center of the circle
Two objects are in circular orbits of different radii around the Sun. Which object has the highest orbital speed?
the one closest to the sun
A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:
the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground.
In an automobile collision, how does an airbag lessen the blow to the passenger? Assume as a result of the collision, the passenger stops.
the stopping impulse is the same for either the hard objects or the airbag. Unlike the windshield or dashboard, the air bag increases the time for the slowing process and thus decreases the average force on the passsenger
A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break. This is because for the egg dropped on the grass:
the time interval for stopping is greater
In a system with two moving objects, when a collision occurs between the objects:
the total momentum is always conserved
Kaitlin uses a bat to hit a thrown baseball. She knocks the ball back in the direction from which it came in a partially inelastic collision. The bat, which is heavier than the baseball, continues to move in the same direction after the hit as Kaitlin "follows through." Is the ball moving faster before or after it was hit?
there is insufficient information to answer this problem
The torque caused by a force F applied at a distance r from the axis of rotation, is given by τ = rFsinθ, where θ is the angle between and . If the magnitudes r and F remain the same, what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?
theta prime = 180-theta
A hoop, solid sphere, and solid cylinder each have the same mass and same radius. When rolling down the same incline, which has the greatest torque from gravity on it?
they all have the same torque
Two blocks are released from the top of a building. One falls straight down while the other slides down a smooth ramp. If all friction is ignored, which one is moving faster when it reaches the bottom?
they both will have the same speed
Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:
upward
Two masses m1 and m2, with m1 = 3 m2, undergo a head-on elastic collision. If the particles were approaching with speed v before the collision, with what speed are they moving apart after collision?
v
The quantity of work equal to one joule is also equivalent to which of the following?
watt * s
Is it possible for the total mechanical energy of a moving particle to be negative?
yes
Suppose the gravitational potential energy for a mass at an altitude of one Earth radius is PE1 and at two Earth radii is PE2. How do the absolute values of these potential energies compare?
|PE1| < 2|PE2|
A car wash nozzle directs a steady stream of water at 1.10 kg/s, with a speed of 30.0 m/s, against a car window. What force does the water exert on the glass? Assume the water does not splash back.
33.0 N
Geosynchronous satellites orbit the Earth at a distance of 42 000 km from the Earth's center. Their angular speed at this height is the same as the rotation rate of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 1 500-kg satellite at this height?
333 N
A meterstick is supported by a knife-edge at the 50.0-cm mark. Doug hangs masses of 0.48 and 0.76 kg from the 10-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.25 kg to keep the stick balanced?
35.6 cm
A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20.0 s. It is then turned off and coasts to a stop in 40.0 s. In the 60.0 s of rotation, through how many revolutions did the fan turn?
377
A non-uniform rod of length L and mass M is pivoted about one end. The moment of inertia of this rod about its pivoted end is 1ML2/4. Attached to the rod is a mass 3M at its midpoint and at the end opposite the pivot is another mass 2M. What is the moment of inertia of this configuration about the pivot?
3ML2
A Hooke's law spring is mounted horizontally over a frictionless surface. The spring is then compressed a distance d and is used to launch a mass m along the frictionless surface. What compression of the spring would result in the mass attaining 4 times the speed received in the situation described here?
4.00d
A simple pendulum, 2.6 m in length, is released with a push when the support string is at an angle of 45.0° from the vertical. If the initial speed of the suspended mass is 1.25 m/s when at the release point, what is its speed at the bottom of the swing? (g = 9.8 m/s2)
4.1 m/s
A girl and her bicycle have a total mass of 46.0 kg. At the top of the hill her speed is 6.0 m/s, and her speed doubles as she rides down the hill. The hill is 15.0 m high and 105 m long. How much kinetic energy and potential energy is lost to friction?
4.3 E +3 J
Preston pushes a wheelbarrow weighing 480 N to the top of a 45.0-m ramp, inclined at 22.0° with the horizontal, and leaves it. Tamara accidentally bumps the wheelbarrow. It slides back down the ramp, during which an 85.0-N frictional force acts on it over the 45.0 m. What is the wheelbarrow's kinetic energy at the bottom at of the ramp? (g = 9.8 m/s2)
4.3 E +3 J
A 26.0-N crate starting at rest slides down a rough 4.8-m-long ramp, inclined at 21.0° with the horizontal. 18 J of energy is lost to friction. What will be the speed of the crate at the bottom of the incline?
4.49 m/s
A 1 000-kg sports car accelerates from zero to 25 m/s in 7.0 s. What is the average power delivered by the automobile engine?
4.5E + 4 W
A solid sphere of mass 2.50 kg and radius 0.120 m starts from rest at the top of a ramp inclined 15.0° and rolls to the bottom. The upper end of the ramp is 1.60 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = MR2 for a solid sphere, and g = 9.80 m/s2.)
4.73 m/s
During a snowball fight two balls with masses of 0.30 and 0.70 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass. The magnitude of initial velocity for each is 12.0 m/s. What is the speed of the 1.0-kg mass immediately after collision?
4.8 m/s
A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.70 m long and each ball on the end is 0.10 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?
4.9E-2 kg·m2
Lonnie pitches a baseball of mass 0.500 kg. The ball arrives at home plate with a speed of 35.0 m/s and is batted straight back to Lonnie with a return speed of 50.0 m/s. If the bat is in contact with the ball for 0.055 s, what is the impulse experienced by the ball?
42.5 N*s
A helicopter stays aloft by pushing large quantities of air downward every second. What mass of air must be pushed downward at 35.0 m/s every second to keep a 1 500-kg helicopter aloft?
420 kg
A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.8 × 10−2 kg·m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.30 m/s, what is its angular speed?
43.0 rad/s
A 35.0-N crate is pulled up a 4.0-m inclined plane by a worker at constant velocity. If the plane is inclined at an angle of 37° to the horizontal and there exists a constant frictional force of 25.0 N between the crate and the surface, what is the force applied by the worker?
46.1 N
An Olympic skier moving at 19.5 m/s down a 17.0° slope encounters a region of wet snow, of coefficient of friction μk = 0.740. How far down the slope does she go before stopping?
46.7 m
The net force acting on a 4.92-kg object is given by Fx = (10 − x) N, where Fx is in newtons and x is in meters. How much work is done on the object as it moves from x = 0 to x = 12.4 m?
47.1 J
A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch the mass. How high does the mass now rise above its starting position?
4h
A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.35 × 104 kg, how many bullets of mass 35.0 g would have to be fired at 200 m/s off the back to give the railroad car a forward velocity of 0.56 m/s?
5.1E +3
A parachutist of mass 50.0 kg jumps out of an airplane at a height of 1 040 m. The parachute deploys, and she lands on the ground with a speed of 4.0 m /s. How much energy was lost to air friction during this jump?
5.1E +5 J
A meter stick is hinged at its lower end and allowed to fall from a vertical position. If its moment of inertia is ML2/3, with what angular speed does it hit the table?
5.42 rad/s
A pile driver drives a post into the ground. The mass of the pile driver is 2 600 kg and it is dropped through a height of 9.0 m on each stroke. If the resisting force of the ground is 4.0 × 106 N, how far is the post driven in on each stroke?
5.7E -2 cm
A point on the rim of a 0.15-m-radius rotating disk has a centripetal acceleration of 5.0 m/s2. What is the angular speed of a point 0.075 m from the center of the disk?
5.8 rad/s
A solid sphere of radius R is placed on an incline that makes an angle θ with the horizontal. The sphere rolls down the incline without slipping. What is its acceleration?
5/7g sin theta
A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?
52 rad/s
A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon. If the value of g on Io is 2.0 m/s2, estimate the speed with which the liquid sulfur left the volcano.
530 m/s
A disk of mass m moving in the positive x direction collides with a stationary disk, also of mass m. The first disk moves in a direction θ1 with respect to the x axis, and the second disk moves off in a direction of θ2 below the x axis, as shown in the figure.
6.1 m/s
An object of mass 0.50 kg weighs 2.0 N when it is 1.0 × 106 m above the surface of Planet X. The radius of the planet is 4.0 × 106 m. What free-fall acceleration will the 0.50-kg object experience when at the surface of Planet X?
6.3 m/s2
What is the minimum amount of energy required for a 60.0-kg climber carrying a 18-kg pack to climb Mt. Everest, 8 250 m high?
6.3E + 6 J
Two hoops or rings (I = MR2) are centered, lying on a turntable. The smaller ring has radius = 0.05 m; the larger has radius = 0.10 m. Both have a mass of 5.0 kg. What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.
6.3E -2 kg*m2
An asteroid has a perihelion (the orbit's closest approach to the Sun) of 1.5 AU and a period of revolution of 8.0 yr. What is its greatest distance from the Sun (its aphelion)?
6.5 AU
Water flows over a section of Niagara Falls at a rate of 1.30 × 106 kg/s and falls 52.0 m. What is the power dissipated by the waterfall?
6.6E + 8 W
A speed boat requires 85.0 kW to move at a constant speed of 14.0 m/s. What is the resistive force of the water at this speed?
6070 N
A 62.0-kg woman runs up a flight of stairs having a rise of 4.28 m in a time of 4.20 s. What average power did she supply?
619 W
What is the angular speed about the rotational axis of the Earth for a person standing on the surface?
7.3 × 10−5 rad/s
A planet has mass M = 8.00 × 1023 kg. The centripetal acceleration of an orbiting space station is equal to the gravitational acceleration on Earth's surface. What is the speed of the space station? (G = 6.67 × 10-11 m3·kg-1·s-2)
7.30 x 10^6 m/s
A planet has mass M = 8.00 × 1023 kg. The centripetal acceleration of an orbiting space station is equal to the gravitational acceleration on Earth's surface. What is the speed of the space station? (G = 6.67 × 10-11 m3·kg-1·s-2)
7.30 × 106 m/s
A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.00-m rod with a mass of 6.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?
7.35 rad/s2
A Ferris wheel, rotating initially at an angular speed of 0.500 rad/s, accelerates over a 10.4-s interval at a rate of 0.040 0 rad/s2. What angular displacement does the Ferris wheel undergo in this 10.4-s interval?
7.4 rad
A 1 300-kg automobile moving at 21 m/s has the brakes applied with a deceleration of 3.0 m/s2. How far does the car travel before it stops?
7.4E +1 m
A 0.30-kg rock is swung in a circular path and in a vertical plane on a 0.25-m-length string. At the top of the path, the angular speed is 12.0 rad/s. What is the tension in the string at that point?
7.9 N
A golf ball hits a wall and bounces back at 3/4 the original speed. What part of the original kinetic energy of the ball did it lose in the collision?
7/16
A spool of thread has an average radius of 1.00 cm. If the spool contains 47.5 m of thread, how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.
756
A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.80 × 10−2 kg·m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.00 m/s, what is its total kinetic energy?
78.4 J
A 7.50-kg bowling ball strikes a 5.20-kg pin. The pin flies forward with a velocity of 4.00 m/s; the ball continues forward at 5.50 m/s. What was the original velocity of the ball?
8.27 m/s
A 3.00-m rod is pivoted about its left end. A force of 7.80 N is applied perpendicular to the rod at a distance of 1.60 m from the pivot causing a ccw torque, and a force of 2.60 N is applied at the end of the rod 3.00 m from the pivot. The 2.60-N force is at an angle of 30.0o to the rod and causes a cw torque. What is the net torque about the pivot? (Take ccw as positive.)
8.58 N*m
An automobile delivers 30.0 hp to its wheels when moving at a constant speed of 24.0 m/s. What is the resistance force on the automobile at this speed? (1 hp = 746 watts)
9.33E +2 N
A box slides down a frictionless incline, and a hoop rolls down another incline. Both inclines have the same height, and both the box and the hoop have the same mass. If both objects start from rest, upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?
Both will have the same kinetic energy, but the box will have the greater speed.
A box is launched up a frictionless incline with an angle of elevation θ. The maximum height reached by the box is h. The box is again launched up the incline with the same initial speed it had before, but this time the angle of elevation has been increased to φ. How does the maximum height H reached this time by the box compare with the previous value h?
H = h
For a point on a spinning disc in uniform circular motion, which of the following is not constant?
Its centripetal acceleration
The Earth's orbit is closest to the Sun in January and farthest from the Sun in July. When is the Earth moving the fastest in orbit?
January
Two masses m1 and m2, with m1 < m2, have momenta with equal magnitudes. How do their kinetic energies compare?
KE1 > KE2
The quantity "angular momentum" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:
ML2T-1
The quantity "angular momentum" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:
ML2T−1.
An object of mass m is on the surface of the Earth. The distance to the Sun and the Moon are dS and dM, and the masses of the Sun and Moon are MS and MM. What is the ratio of the gravitational force from the Sun to that of the Moon on the object?
MSd2M /MMd2M
