Final Test

Which of the following ranges corresponds to the longest wavelengths, infrasonic, audible, or ultrasonic?

(infrasonic)

If ሬԦ = (3 m)ଙ̂− (4 m)ଚ̂, and ሬԦ = (2 N) ,find ሬԦ = ሬԦ × ሬԦ. (ሬԦ =

(-6 m) i - (8 m)j

Alex, parked by the side of an east-west road, is watching car P, which is moving in a westerly direction. Barbara, driving east at a speed 52 km/h, watches the same car. Take the easterly direction as positive. If Alex measures a speed of 78 km/h for car P, what velocity will Barbara measure?

(-130 km/h)

What is the emissivity of an ideal reflector?

(0)

I drop a 60-g golf ball from 2.0 m high. It rebounds to 1.5 m. How much energy is lost?

(0.29 J)

If two adjacent frequencies of an organ pipe closed at one end are 550 Hz and 650 Hz, what is the length of the organ pipe? (vsound = 340 m/s)

(1.70 m)

A particle of mass 1.5 kg is moving at 3 m/s along the line y = 3 m. What is its angular momentum about the origin?

(13.5 kg∙m2 /s)

A large spring requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring?

(15 000 N/m)

A swimming pool heater has to be able to raise the temperature of the 40 000 gallons of water in the pool by 15.0 C. How many kilowatt-hours of energy are required? (One gallon of water has a mass of approximately 3.8 kg and the specific heat of water is 4 186 J/kgC.)

(2 650 kWh)

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the acceleration magnitude when t = 3 s?

(25.3 m/s2 )

A 2.0-m long piano string of mass 10 g is under a tension of 338 N. Find the speed with which a wave travels on this string.

(260 m/s)

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s2 . What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

(30 m/s2 )

A rock is thrown straight up with an initial velocity of 24.5 m/s.What maximum height will the rock reach before starting to fall downward? Take acceleration due to gravity as 9.80 m/s2 .

(30.6 m)

A car drives around a curve with radius 400 m at a speed of 32 m/s. The road is banked at 7.0 degree. The mass of the car is 1500 kg. What is the magnitude of the centripetal force in order to make this turn?

(3800 N)

The moment of inertia of a rod of mass M and length L about an axis perpendicular to the rod at one end is ML2 /3. What is its moment of inertia about an axis perpendicular to the rod a third of the way from one end?

(4ML2 /9)

A sphere of mass 3.2 kg and radius 4.57 cm rolls without slipping down a 27° incline from a height of 30 cm above the floor. When it reaches the bottom, the center of mass of the sphere is moving at 6.4 m/s. What is its rotational kinetic energy when it reaches the floor?

(5.4 J)

A 7.0-kg bowling ball strikes a 2.0-kg pin. The pin flies forward with a velocity of 6.0 m/s; the ball continues forward at 4.0 m/s. What was the original velocity of the ball?

(5.7 m/s)

A 20 kg box slides down a 12.0 m long frictionless incline at an angle of 30 degrees with the horizontal. A force of 50 N is applied to the box to try to pull it up the incline. The applied force makes an angle of 10 degrees to the incline and above the incline. What is the increase in the kinetic energy of the box?

(585 J)

An inventor develops a stationary cycling device by which an individual, while pedaling, can convert all of the energy expended into heat for warming water. How much mechanical energy is required to increase the temperature of 300 g of water (enough for 1 cup of coffee) from 25C to 90C? (1 cal = 4.186 J, the specific heat of water is 4 186 J/kgC)

(82 000 J)

A drag racer starts from rest and accelerates at 10 m/s2 for the entire distance of 400 m (1/4 mile). What is the velocity of the race car at the end of the run?

(89 m/s)

How large a force is necessary to stretch a 2.5-mm-diameter steel wire (Y = 2.0 1011 N/m2 ) by 1.0%?

(9.8 * 10^3 N)

The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz. What wavelength in air at room temperature is associated with this frequency?

(Assume the speed of sound to be 340 m/s.) (1.7 cm)

Three identical springs each have the same spring constant k. If these three springs are attached end to end forming a spring three times the length of one of the original springs, what will be the spring constant of the combination?

(k/3)

Which type of heating causes sunburn?

(radiation)

A rock, released at rest from the top of a tower, hits the ground after 1.5 s. What is the speed of the rock as it hits the ground? Ignore air resistance.

(15 m/s)

When a drag strip vehicle reaches a velocity of 60 m/s, it begins a negative acceleration by releasing a drag chute and applying its brakes. While reducing its velocity back to zero, its acceleration along a straight line path is a constant 7.5 m/s2 . What displacement does it undergo during this deceleration period?

(240 m)

Two billiard balls have velocities of 2.0 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)

Masses are distributed in the xy-plane as follows: 10 kg at (2.0, 6.0) m, 4.0 kg at (2.0, 0.0) m, and 6.0 kg at (0.0, 3.0) m. Where would a 20-kg mass need to be positioned so that the center of gravity of the resulting four mass system would be at the origin?

(-1.4m, -3.9m)

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

(-2)

A 0.20-kg object is oscillating on a spring with a spring constant of k = 15 N/m. What is the potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude?

(0.012 J)

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement is a maximum (hence x = 8 cm when t = 0), what is the displacement of the mass when t = 3.7 s?

(0.025 m)

A 0.2-kg aluminum plate, initially at 20C, slides down a 20-m-long surface, inclined at a 30 angle to the horizontal. The force of kinetic friction exactly balances the component of gravity down the plane so that the plate, once started, glides down at constant velocity. If 90% of the mechanical energy of the system is absorbed by the aluminum, what is its temperature increase at the bottom of the incline? (Specific heat for aluminum is 900 J/kgC.)

(0.10 C)

Equal wavelength waves of amplitude 0.25 m and 0.15 m interfere with one another. What is the resulting minimum amplitude that can result?

(0.10 m)

A 20-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 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?

(0.16 kJ)

A child sits on a swing supported by ropes of length 3.0 m. With what frequency will she need to apply the driving force to maintain swinging?

(0.29 Hz)

A waterfall is 150 m high. What is the increase in water temperature at the bottom of the falls if all the initial potential energy goes into heating the water? (g = 9.8 m/s2 , cw = 4 186 J/kgC)

(0.35C)

An automobile gas tank is filled to its capacity of 15.00 gallons with the gasoline at an initial temperature of 15C. The automobile is parked in the sun causing the gasoline's temperature to rise to 50C. If the coefficient of volume expansion for gasoline is 9.6 104 /C, what volume runs out the overflow tube? Assume the change in volume of the tank is negligible.

(0.50 gallons)

If I triple the mass per unit length of guitar string, its natural frequency changes by what factor?

(0.58)

The thermal conductivity of aluminum is 238 J/s·m·ºC and of copper is 397 J/s·m·ºC. A rod of each material is used as a heat conductor. If the rods have the same geometry and are used between the same temperature differences for the same time interval, what is the ratio of the heat transferred by the aluminum to the heat transferred by the copper?

(0.599)

A 75-kg swimmer dives horizontally off a 500-kg raft. If the diver's speed immediately after leaving the raft is 4 m/s, what is the corresponding raft speed?

(0.6 m/s)

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-s interval?

(0.60 m/s2 )

Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the center of gravity when she sits on one end of the board. How far is she from the support point?

(0.67 m)

Two loudspeakers are placed side by side and driven by the same source at 500 Hz. A listener is positioned in front of the two speakers and on the line separating them, thus creating a constructive interference at the listener's ear. If one of the speakers is gradually pushed toward the listener, how far must it be moved to repeat the condition of constructive interference at the listener's ear? The speed of sound = 340 m/s.

(0.68 m)

A cannon of mass 1 500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 45 above the horizontal. Find the recoil velocity of the cannon across the level ground.

(0.94 m/s)

How far away is a lightning strike if you hear the thunderclap 3.00 s after you see the lightning bolt strike? (vsound = 340 m/s, vlight = 3 108 m/s)

(1 020 m)

A 2 500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers. The two continue to move together at 7.00 m/s. What was the mass of the struck car?

(1 070 kg)

. If a guitar string has a fundamental frequency of 500 Hz, what is the frequency of its second overtone?

(1 500 Hz)

A high-diver of mass 70 kg jumps off a board 10 m above the water. If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

(1 666 N)

A tuning fork is sounded above a resonating tube (one end closed), which resonates at a length of 0.20 m and again at 0.60 m. If the tube length were extended further, at what point will the tuning fork again create a resonance condition?

(1.0 m)

Consider two steel rods, A and B. B has three times the area and twice the length of A, so Young's modulus for B will be what factor times Young's modulus for A?

(1.0)

A hoop of radius 1.0 m is placed in the first quadrant of a xy-coordinate system with its rim touching both the x-axis and the y-axis. What are the coordinates of its center of gravity?

(1.0m, 1.0m)

A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?

(1.1 m/s2 )

A brass cube, 10 cm on a side, is raised in temperature by 200C. The coefficient of volume expansion of brass is 57 106 /C. By what percentage does volume increase?

(1.1%)

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0, 0.0) m, 4.0 kg at (2.0, 0.0) m, and 5.0 kg at (2.0, 3.0) m. What is the x-coordinate of the center of gravity of this system of masses?

(1.2 m)

Doubling the tension in a guitar string will change its natural frequency by what factor?

(1.4)

If the kinetic energy of a ball is doubled, what happens to the momentum of the ball?

(1.41 times larger)

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

(1.6 rad/s2 )

A mechanic using a 25-cm long wrench to loosen a bolt applies a 50-N force to the end of the wrench and manages to generate a torque 625 N∙cm on the bolt. What is his effective lever arm?

(12.5 cm)

A 50-g ball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the average acceleration of the ball during this time interval?

(13 400 m/s2 )

A 3.00-g lead bullet is traveling at a speed of 300 m/s when it embeds in a wood post. If we assume that half of the resultant heat energy generated remains with the bullet, what is the increase in temperature of the embedded bullet? (specific heat of lead = 0.030 5 kcal/kgC, 1 kcal = 4 186 J)

(176C )

A 20-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. If the block had been originally at rest and is free to move, what is its resulting speed?

(18 m/s)

A horizontal 735-N merry-go-round is a solid disk of radius 1.50 m with a moment of inertia of 169 kg∙m2 about its axis. It is started from rest by a constant horizontal force of 55 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 3.00 s.

(181 J)

A rocket of total mass M and with burnout mass 0.20 M attains a speed of 3 200 m/s after starting from rest in deep space. What is the exhaust velocity of the rocket?

(2 000 m/s)

What is the intensity of a sound with a measured intensity level of 84 dB? (I0 = 1012 W/m2 )

(2.5 104 W/m2 )

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)

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 550 N in that rope?

(2.5 m)

A 0.20-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal frictionless surface. At the instant that it is displaced from equilibrium by 0.050 m, what is its acceleration?

(2.5 m/s2 )

The bicycle wheel shown has a mass of 2.0 kg and a radius of 71 cm. It is initially spinning with an angular velocity of -3.5 s-1 in the −ଙ̂ direction. The distance from the center-of-mass of the wheel to the frictionless support pivot at O is 14 cm. What is the rate-of-change of the angular momentum vector at the moment the wheel is released to freely pivot about O?

(2.7 kg∙m2 /s/s)

A 4.0 kg ball is moving at 3.0 m/s to the NORTH and a 5.0 kg ball is moving at 2.0 m/s to the NORTHWEST. What is the total momentum of the system?

(20.3 kg m/s at an angle of 69.7 degrees NORTH of WEST)

The intensity level of sound 20 m from a jet airliner is 120 dB. At what distance from the airplane will the sound intensity level be a tolerable 100 dB? Assume spherical spreading of sound.

(200 m)

What centripetal force does an 80-kg passenger experience when seated 12 m from the center of a Ferris wheel whose angular speed is 0.50 rad/s?

(240 N)

Two tuning forks sounding together result in a beat frequency of 3 Hz. If the frequency of one of the forks is 256 Hz, what is the frequency of the other?

(259 Hz or 253 Hz)

A flute behaves like a tube open at both ends. If its length is 65.3 cm, and the speed of sound is 340 m/s, what is its fundamental frequency in Hz?

(260 Hz)

A 30 kg mass falls from a height of 4.0 m. What is the momentum of the mass just before it hits the ground?

(265.6 kg m/s)

A temperature change from 20C to 35C corresponds to what incremental change in F?

(27)

A 3.0-m2 Thermopane window is constructed, using two layers of glass 4.0 mm thick, separated by an air space of 5.0 mm. If the temperature difference is 20 C from the inside of the house to the outside air, what is the rate of heat flow through this window? (Thermal conductivity for glass is 0.84 J/smC and for air 0.023 4 J/smC.)

(270 W)

Among the frequencies listed, 33 Hz, 330 Hz, 3 300 Hz, and 33 000 Hz, which is the one that the human ear most sensitive?

(3 300 Hz)

A 100-W light bulb is left on for 10.0 hours. Over this period of time, how much energy was used by the bulb?

(3 600 000 J)

The density of a certain metal solid is 7.2 103 kg/m3 , and its Young's modulus is 10 1010 N/m2 . What is the speed of sound in this metal?

(3 700 m/s)

During a snowball fight two balls with masses of 0.4 and 0.6 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 15 m/s. What is the speed of the 1.0-kg mass immediately after collision?

(3 m/s)

A uniform 1.0-N meter stick is suspended horizontally by vertical strings attached at each end. A 2.0-N weight is suspended from the 10-cm position on the stick, another 2.0-N weight is suspended from the 50 cm position, and a 3.0-N weight is suspended from the 60 cm position. What is the tension in the string attached at the 100-cm end of the stick?

(3.5 N)

At liftoff, the engines of the Saturn V rocket consumed 13 000 kg/s of fuel and exhausted the combustion products at 2 900 m/s. What was the total upward force (thrust) provided by the engines?

(3.77 107 N)

A spring-powered dart gun is un-stretched and has a spring constant 12.0 N/m. The spring is compressed by 8.0 cm and a 5.0 gram projectile is placed in the gun. What is the velocity of the projectile when it is shot from the gun?

(3.92 m/s)

. A meter stick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 20-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

(30 cm)

A plane is traveling at Mach 0.950 through air at a temperature of 0C. What is the plane's speed? Speed of sound at 0ºC is 331 m/s.

(314 m/s)

The speed of sound at 0C is 331 m/s. What is the speed of sound at 25C? (0C = 273 K)

(346 m/s)

A solar heating system has a 25.0% conversion efficiency; the solar radiation incident on the panels is 1 000 W/m2 . What is the increase in temperature of 30.0 kg of water in a 1.00-h period by a 5.00-m2 -area collector? (cw = 4 186 J/kgC)

(35.8C)

A 4.0 kg ball is traveling at 5.0 m/s and strikes a wall. The 4.0 kg ball bounces off the wall with a velocity of 4.0 m/s. What is the change in momentum of the ball?

(36 kg m/s)

What is the temperature increase of 4.0 kg of water when heated by a 1000-W immersion heater for 10 min? (cw = 4 186 J/kgC)

(36C)

You stand by the railroad tracks as a train passes by. You hear a 1 000-Hz frequency when the train approaches, which changes to 800 Hz as it goes away. How fast is the train moving? The speed of sound in air is 340 m/s.

(37.8 m/s)

The surface of the Sun has a temperature of about 5 800 K. If the radius of the Sun is 7 108 m, determine the power output of the sun. (Take e = 1, and = 5.67 108 W/m2 K 4 ).

(4.0 1026 W)

If it takes 4.0 N to stretch a spring 6.0 cm and if the spring is then cut in half, what force does it take to stretch one of the halves 3.0 cm?

(4.0 N)

A 4.0 kg object is moving at 5.0 m/s NORTH. It strikes a 6.0 kg object at rest. The objects have an elastic collision and move is the NORTH or SOUTH direction. What is the velocity of the 6.0 kg object after the collision?

(4.0 m/s NORTH)

Tripling the power output from a speaker emitting a single frequency will result in what increase in loudness?

(4.8 dB)

A 1 000-kg sports car accelerates from zero to 25 m/s in 7.5 s. What is the average power delivered by the automobile engine?

(41.7 kW)

A windowpane is half a centimeter thick and has an area of 2.0 m2 . The temperature difference between the inside and outside surfaces of the pane is 15 C. What is the rate of heat flow through this window? (Thermal conductivity for glass is 0.84 J/smC.)

(5 000 W)

A solar heated house loses about 5.4 107 cal through its outer surfaces on a typical 24-h winter day. What mass of storage rock is needed to provide this amount of heat if it is brought up to initial temperature of 70C by the solar collectors and the house is maintained at 20C? (Specific heat of rock is 0.21 cal/gC.)

(5 100 kg)

A rectangular steel plate with dimensions of 30 cm 25 cm is heated from 20C to 320C. What is its change in area? (Coefficient of linear expansion for steel is 11 106 /C.)

(5.0 cm2 )

The lower A on a piano has a frequency of 27.5 Hz. If the tension in the 2.0-m-long string is 304 N and one-half wavelength occupies the string, what is the mass of the string?

(50 g)

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 60-kg woman runs up a flight of stairs having a rise of 4.0 m in a time of 4.2 s. What average power did she supply?

(560 W)

A 0.20 kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.080 m. What is its speed at the instant when its displacement is 0.040 m?

(57 cm/s)

Water flows over a section of Niagara Falls at a rate of 1.20 106 kg/s and falls 50.0 m. What is the power dissipated by the waterfall?

(588 MW)

A copper wire of length 2.5 m, cross sectional area 7.1 106 m2 and Young's modulus 11 1010 N/m2 has a 200-kg load hung on it. What is its increase in length?

(6.3 mm)

A uniform pressure of 9.0 105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 1010 N/m2 )

(6.4*10^4 %)

A steel wire, 150 m long at 10C, has a coefficient of linear expansion of 11 106 /C. Find its change in length as the temperature changes from 10C to 50C.

(6.6 cm)

An object at 27C has its temperature increased to 32C. The power then radiated by this object increases by how many percent?

(6.8%)

Alex throws a 0.15-kg rubber ball down onto the floor. The ball's speed just before impact is 6.5 m/s, and just after is 3.5 m/s. If the ball is in contact with the floor for 0.025 s, what is the magnitude of the average force applied by the floor on the ball?

(60 N)

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in 40 s. In the one minute of rotation, through how many revolutions did the fan turn?

(60)

Transverse waves travel with a speed of 200 m/s along a taut copper wire that has a diameter of 1.50 mm. What is the tension in the wire? (The density of copper is 8.93 g/cm3 .)

(631 N)

The graph shows the force on an object as it moves a distance x. What is the work done by the force when the object moves from 0.0 m to 10.0 m?

(64 J)

A C note (f = 256 Hz) is sounded on a piano. If the length of the piano wire is 1.00 m and its mass density is 2.50 g/m, what is the tension in the wire?

(655N)

A mechanic using a 20-cm long wrench to loosen a bolt applies a 30-N force to the end of the wrench and manages to generate a torque 544 N∙cm on the bolt. What is the acute angle between his arm and the wrench?

(65°)

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

(7.3 105 rad/s)

A 0.30-kg rock is swung in a circular path and in a vertical plane on a 0.25-mlength 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 railroad freight car, mass 20 000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50 000-kg loaded second car, initially at rest and with brakes released. What percentage of the initial kinetic energy of the 20 000-kg car is preserved in the two-coupled cars after collision?

(71%)

. Starting from rest, a sphere of mass 3.2 kg and radius 4.57 cm rolls without slipping down a 27° incline from a height of 30 cm above the floor. What is its total kinetic energy when it reaches the floor?

(9.4 J)

At high noon, the sun delivers 1 000 W to each square meter of a blacktop road. What is the equilibrium temperature of the hot asphalt, assuming its emissivity e = 1? ( = 5.67 108 W/m2 K 4 )

(91C)

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, what happens to the power delivered to it by the force? It remains the same, increases, or decreases?

(Increases)

When the standing wave pattern in a pipe is NANA (N stands for nodes, A for antinodes), what type of the pipe is this?

(It is open at one end and closed at the other end.)

Suppose there is an object for which F = +kx. What will happen if the object is moved away from equilibrium (x = 0) and released?

(It will move further away with increasing acceleration)

If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's, where the acceleration due to gravity is one-sixth (1/6) that on the Earth, by what factor would the pendulum frequency be changed?

(about 0.41)

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s. As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops. In what final direction does the first ball move?

(at an angle of 53.1o ccw from the x-direction

A bicycle wheel is mount on an axle with a handle as shown above. The wheel is initially held stationary while it is being spun. If the angular velocity of the wheel is in the ଙ̂ direction, and the wheel is released so that it can pivot freely about the support point at O, what will be the direction of the precessional motion about O? (gravity acts in the −ଚ direction)

(in the −k direction)

A bicycle wheel is mount on an axle with a handle as shown below. The wheel is initially held stationary while it is being spun. If the angular velocity of the wheel is in the ଙ̂ direction, and the wheel is released so that it can pivot freely about the support point at O, what will be the direction of the net torque about O? (gravity acts in the −ଚ̂ direction)

(in the −k direction)

An airplane flying with a constant speed flies from a warm air mass into a cold air mass. The Mach number will increase, decrease, or stay the same?

(increase)

A skater cuts her moment of inertia in half by pulling her arms and legs in. By how much does her angular velocity change?

(it doubles)

An object of mass m moving at speed v0 strikes and 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?

(it increases by mv2 )

For a standing wave in an air column in a pipe that is open at both ends, what are the least amount of nodes and antinodes in the pipe?

(two antinodes and one node)

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the speed of the mass when t = 3 s?

(zero)

An elevator weighing 20 000 N is supported by a steel cable. What is the tension in the cable when the elevator is being accelerated upward at a rate of 3.00 m/s2?

(26 100 N)

A hiker walks 200 m west and then walks 100 m north. In what direction is her resulting displacement?

(26.6 N of W)

A stone is thrown with an initial speed of 15 m/s at an angle of 53 above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, then what is the speed of the rock as it hits the ground?

(30 m/s)

A car drives around a curve with radius 400 m at a speed of 32 m/s. The road is not banked. The mass of the car is 1500 kg. What is the frictional force on the car?

(3800 N)

A rock is thrown straight up with an initial velocity of 19.6 m/s. What time interval elapses between the rock's being thrown and its return to the original launch point?

(4.00 s)

A 20-N crate starting at rest slides down a rough 5.0-m long ramp, inclined at 25 with the horizontal. 20 J of energy is lost to friction. What will be the speed of the crate at the bottom of the incline?

(4.7 m/s)

What angular speed (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm?

(40.7 rev/s)

A roller coaster, loaded with passengers, has a mass of 2 500 kg; the radius of curvature of the track at the top point is 20 m. If the vehicle has a speed of 25 m/s at this point, what force is exerted on the vehicle by the track?

(5.4 104 N)

A hill is 100 m long and makes an angle of 12 with the horizontal. As a 50-kg jogger runs up the hill, how much work does gravity do on the jogger?

(-10 000 J)

A 5.0 kg box slides up a 10 m long frictionless incline at an angle of 20 degrees with the horizontal pushed by a 40 Newton force parallel to the incline. What is the change in kinetic energy?

(232 J)

Three identical 6.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 2.0 m/s2 . What is the magnitude of the force exerted on the middle cube by the left cube in this case?

(24 N)

A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30.0 north of east. What is the new velocity and direction of the aircraft?

(607 mph, 5.67 N of E)

The following force vectors act on an object: i) 50.0 newtons at 45.0 north of east and ii) 25.0 newtons at 30.0 south of east. What is the magnitude of the resultant force and its angle relative to the easterly direction?

(61.4 newton at 21.8)

A string attached to an airborne kite is maintained at an angle of 40 with the horizontal. If a total of 120 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process? Assume the kite string doesn't sag.

(92 m)

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher. At what point is the ball's speed at a minimum? Ignore air resistance.

(at the top of the trajectory)

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 the same compression d, the spring is now used to launch a mass of 2m. How high does this second mass rise?

(h/2)

A 5 000-N weight is suspended in equilibrium by two cables. Cable 1 applies a horizontal force to the right of the object and has a tension, T1. Cable 2 applies a force upward and to the left at an angle of 37.0 to the negative x axis and has a tension, T2. Find T2

(8 310 N)

An object moves 20 m east in 30 s and then returns to its starting point taking an additional 50 s. If west is chosen as the positive direction, what is the sign associated with the average velocity of the object?

(0, no sign)

A 100-kg box is placed on a ramp. As one end of the ramp is raised, the box begins to move downward just as the angle of inclination reaches 15. What is the coefficient of static friction between box and ramp?

(0.27)

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping?

(0.28)

An object moves 20 m east in 30 s and then returns to its starting point taking an additional 50 s. If west is chosen as the positive direction, what is the average speed of the object?

(0.50 m/s)

A 7.0-kg bowling ball experiences a net force of 5.0 N. What will be its acceleration?

(0.71 m/s2)

A 500-N tightrope walker stands at the center of the rope such that each half of the rope makes an angle of 10.0 with the horizontal. What is the tension in the rope?

(1 440 N)

Two ropes are attached to a 40-kg object. The first rope applies a force of 25 N and the second, 40 N. If the two ropes are perpendicular to each other, what is the resultant acceleration of the object?

(1.2 m/s2 )

A horizontal force of 750 N is needed to overcome the force of static friction between a level floor and a 250-kg crate. What is the acceleration of the crate if the 750-N force is maintained after the crate begins to move and the coefficient of kinetic friction is 0.12?

(1.8 m/s2 )

A baseball is released at rest from the top of the Washington Monument. It hits the ground after falling for 6.0 s. What was the height from which the ball was dropped? Ignore air resistance.

(1.8 x 102 m)

Two blocks of masses 20 kg and 8 kg are connected together by a light string and rest on a frictionless level surface. Attached to the 8-kg mass is another light string, which a person uses to pull both blocks horizontally. If the two-block system accelerates at 0.5 m/s2 what is the tension in the connecting string between the blocks?

(10 N)

A 0.400-kg object is swung in a circular path and in a vertical plane on a 0.500-mlength 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?

(16.7 N)

A ball is pushed with an initial velocity of 4.0 m/s. The ball rolls down a hill with a constant acceleration of 1.6 m/s2 . The ball reaches the bottom of the hill in 8.0 s. What is the ball's velocity at the bottom of the hill?

(17 m/s)

A European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 8.00 s. What is the speed after the first 5.00 s of acceleration?

(17.4 m/s)

The end of the cutting cord on a gas-powered weed cutter is 0.15 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?

(19 m/s)

A block of mass 5.00 kg rests on a horizontal surface where the coefficient of sliding kinetic friction between the two is 0.200. A string attached to the block is pulled horizontally, resulting in a 2.00-m/s2 acceleration by the block. Find the tension in the string.

(19.8 N)

A girl and her bicycle have a total mass of 40.0 kg. At the top of the hill her speed is 5.0 m/s, and her speed doubles as she rides down the hill. The hill is 10.0 m high and 100 m long. How much kinetic energy and potential energy is lost to friction?

(2 420 J)

A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails with magnitude of 6 000 N directed toward the northwest (45 N of W). What is the magnitude of the resultant acceleration?

(2.2 m/s2 )

A 10.0-kg box starts at rest and slides 3.5 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?

(3.5 m/s)

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?

(339 N)

A sled weighs 100 N. It is held in place on a frictionless 20 slope by a rope attached to a stake at the top; the rope is parallel to the slope. Find the tension in the rope.

(34 N)

A 1 200-kg automobile moving at 25 m/s has the brakes applied with a deceleration of 8.0 m/s2 . How far does the car travel before it stops?

(39 m)

A 20-kg traffic light hangs midway on a cable between two poles 40 meters apart. If the sag in the cable is 0.40 meters, what is the tension in each side of the cable?

(4 900 N)

A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s2 . What is the angular speed of the wheel?

(4.0 rad/s)

A pile driver drives a post into the ground. The mass of the pile driver is 2 500 kg and it is dropped through a height of 8.0 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?

(4.9 cm)

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. 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?

(40 m/s2 )

A cart is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 2.0 m/s2 . What is the magnitude of the cart's displacement during the first 6.0 s of its motion?

(66 m)

A 120 Newton box is at rest on an incline of 35 degrees. The surface of the incline is frictionless and a rope is attached to the box and exerts a force on the box that is 10 degree above the incline. What is the force exerted by the rope on the box?

(69.9 N)

A 2000 kg car is traveling on a banked curved icy road. The velocity of the car is 25 m/s and the road has a radius of curvature of 500 m. If the car is to travel on the icy road without sliding, what is the angle of the banked road?

(7.27)

A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails with magnitude of 6 000 N directed toward the northwest (45 N of W). What is the direction of the resultant acceleration?

(74 N of W)

Find the tension in an elevator cable if the 1 000-kg elevator is descending with an acceleration of 1.8 m/s2 , downward.

(8 000 N)

A 500-N tightrope walker stands at the center of the rope. If the rope can withstand a tension of 1 800 N without breaking, what is the minimum angle the rope can make with the horizontal?

(8)

A taxicab moves five blocks due north, five blocks due east, and another two blocks due north. Assume all blocks are of equal size. What is the magnitude of the taxi's displacement, start to finish?

(8.6 blocks)

A horizontal force is applied to a 4.0 kg box. The box starts from rest moves a horizontal distance of 8.0 meters and obtains a velocity of 6.0 m/s. The system is frictionless. What is the horizontal force?

(9 N)

A horizontal force of 200 N is applied to a 55-kg cart across a 10-m level surface. If the cart accelerates at 2.0 m/s2 , then what is the work done by the force of friction as it acts to retard the motion of the cart?

(-900 J)

A horizontal force of 750 N is needed to overcome the force of static friction between a level floor and a 250-kg crate. If g = 9.8 m/s2 , what is the coefficient of static friction?

(0.31)

Which one, temperature, velocity, acceleration, or displacement, is not a vector quantity?

temperature

A Cessna aircraft has a lift-off speed of 120 km/hr. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m?

(2.31 m/s2 )

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 with respect to the horizontal. What is the maximum vertical displacement that the ball reaches during its trajectory?

(11.0 m)

A cheetah can run at approximately 100 km/hr and a gazelle at 80.0 km/hr. If both animals are running at full speed, with the gazelle 70.0 m ahead, how long before the cheetah catches its prey?

(12.6 s)

The value of an object's acceleration may be characterized in equivalent words by what?

(rate of change of velocity)

A v vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the acceleration of the ball is zero. What is the velocity of the ball at t = 5 s?

(the velocity of the ball is not changing)

At what speed will a car round a 52-m-radius curve, banked at a 45 angle, if no friction is required between the road and tires to prevent the car from slipping?

(23 m/s)

An astronaut applies a force of 500 N to an asteroid and it accelerates at 7.00 m/s2 . What is the asteroid's mass?

(71 kg)

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4.0 106 m. What is the mass of Planet X? (G = 6.67 1011 N m2 /kg2 )

(9.6 1024 kg)

A plane is moving due north, directly towards its destination. Its airspeed is 200 mph. A constant breeze is blowing from west to east at 30 mph. At what rate is the plane moving north?

(198 mph)

A boat moves at 10.0 m/s relative to the water. If the boat is in a river where the current is 2.00 m/s, how long does it take the boat to make a complete round trip of 1 000 m upstream followed by a 1 000-m trip downstream?

(208 s)

Human reaction time is usually about 0.20 s. If your lab partner holds a ruler between your finger and thumb and releases it without warning, how far can you expect the ruler to fall before you catch it?

(20 cm)

Three identical 6.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 2.0 m/s2 . What is the magnitude of the force exerted on the right cube by the middle cube in this case?

(12 N)

Two blocks, joined by a string, have masses of 6.0 and 9.0 kg. They rest on a frictionless horizontal surface. A 2nd string, attached only to the 9-kg block, has horizontal force = 30 N applied to it. Both blocks accelerate. Find the tension in the string between the blocks

(12 N)

A stone is thrown at an angle of 30 above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s. What is the height of the cliff? (Ignore air resistance.

(120 m)

A jogger runs halfway around a circular path with a radius of 60 m. What, respectively, are the magnitude of the displacement and the distance jogged?

(120 m, 188 m)

A stone is thrown with an initial speed of 15 m/s at an angle of 53 above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, what is the magnitude of the horizontal displacement of the rock?

(38 m)

A stone is thrown at an angle of 30 above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s. How far out from the cliff's edge does the stone travel horizontally? Ignore air resistance.

(58 m)

Two blocks of masses 20 kg and 8.0 kg are connected together by a light string and rest on a frictionless level surface. Attached to the 8-kg mass is a second light string, which a person uses to pull both blocks horizontally. If the two-block system accelerates at 0.5 m/s2 , what is the tension in the second string attached to the 8-kg mass?

(14 N)

A girl is using a rope to pull a box that weighs 300 N across a level surface with constant velocity. The rope makes an angle of 30 above the horizontal, and the tension in the rope is 100 N. What is the normal force of the floor on the box?

(250 N)

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)

A stone is thrown with an initial speed of 15 m/s at an angle of 53 above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, then what is the magnitude of the vertical velocity component of the rock as it hits the ground?

(29 m/s)

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 European sports car dealer claims that his car will accelerate at a constant rate from rest to 100 km/hr in 8.00 s. If so, what is the acceleration?

(3.47 m/s2 )

A 15-kg block rests on a level frictionless surface and is attached by a light string to a 5.0-kg hanging mass where the string passes over a massless frictionless pulley. If g = 9.8 m/s2 , what is the tension in the connecting string?

(37 N)

Doug hits a hockey puck, giving it an initial velocity of 6.0 m/s. If the coefficient of kinetic friction between ice and puck is 0.050, how far will the puck slide before stopping?

(37 m)

A boxcar of mass 200 tons at rest becomes uncoupled on a 2.5 grade. If the track is considered to be frictionless, what speed does the boxcar have after 10 seconds?

(4.3 m/s)

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?

(4.7 104 N)

A 5 000-N weight is held suspended in equilibrium by two cables. Cable 1 applies a horizontal force to the right of the object and has a tension, T1. Cable 2 applies a force upward and to the left at an angle of 37.0 to the negative x axis and has a tension, T2. What is the tension, T1?

(6 640 N)

A 10-kg mass and a 2.0-kg mass are connected by a light string over a massless, frictionless pulley. If g = 9.8 m/s2 , what is the acceleration of the system when released?

(6.5 m/s2 )

As a 3.0-kg bucket is being lowered into a 10-m-deep well, starting from the top, the tension in the rope is 9.8 N. What is the acceleration of the bucket?

(6.5 m/s2 downward)

A railroad train travels forward along a straight track at 80.0 m/s for 1 000 m and then travels at 50.0 m/s for the next 1 000 m. What is the average velocity?

(61.5 m/s)

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)

John throws a baseball from the outfield from shoulder height, at an initial velocity of 29.4 m/s at an initial angle of 30.0 with respect to the horizontal. The ball is in its trajectory for a total interval of 3.00 s before the third baseman catches it. Ignore the air resistance. What is the ball's horizontal displacement?

(76.4 m)

A river flows due east at 3.0 m/s. A boat crosses the 300-m-wide river by maintaining a constant velocity of 10 m/s due north relative to the water. If no correction is made for the current, how far downstream does the boat move by the time it reaches the far shore?

(90 m)

A sled weighs 100 N. It is held in place on a frictionless 20 slope by a rope attached to a stake at the top; the rope is parallel to the slope. What is the normal force of the slope acting on the sled?

(94 N)

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30 with the ground. What are the parallel and perpendicular components, respectively, of this force with respect to the ground?

(95 N, 55 N)

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 with respect to the horizontal. If it is in its trajectory for a total of 3.00 s before being caught by the third baseman, what is the ball's net vertical displacement during its 3-s trajectory?

(zero)