Physics 2010 final

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)

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)

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)

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

(0.71 m/s2 )

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

(1 500 Hz)

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)

An 80-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 20 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.

(170 N)

A 2.0-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.)

(180 W)

A quantity of a monatomic ideal gas expands to twice the volume while maintaining the same pressure. If the internal energy of the gas were U0 before the expansion, what is it after the expansion?

(2 U0)

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)

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 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 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 hot (70C) lump of metal has a mass of 250 g and a specific heat of 0.25 cal/gC. John drops the metal into a 500-g calorimeter containing 75 g of water at 20C. The calorimeter is constructed of a material that has a specific heat of 0.10 cal/ gC. When equilibrium is reached, what will be the final temperature? cwater = 1.00 cal/gC.

(37C)

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 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)

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 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 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 45C.

(5.8 cm)

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 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)

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 12.4 + 11 + 67.37 + 4.201?

(95)

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 10.5 *8.8 * 3.14?

290

Calculate (0.82 + 0.042) (4.4 103 ), keeping only significant figures.

3 800

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)

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)

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 )

Iced tea is made by adding ice to 1.8 kg of hot tea, initially at 80C. How many kg of ice, initially at 0C, are required to bring the mixture to 10C? (Lf = 3.33 x 105 J/kg, cw = 4 186 J/kgC)

(1.4 kg)

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)

. An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth. A P-wave travels at 8 000 m/s and an S-wave at 4 000 m/s. If P-waves are received at a seismic station 30.0 s before an S-wave arrives, how far is the station from the earthquake center?

(240 km)

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 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)

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)

. 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 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 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 0.12-kg ball is moving at 6 m/s when it is hit by a bat, causing it to reverse direction and have a speed of 8 m/s. What is the change in the magnitude of the momentum of the ball?

(1.68 kg m/s)

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 20C to 95C? (1 cal = 4.186 J, the specific heat of water is 4 186 J/kgC)

(94 000 J)

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)

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 3.0 inches, respectively. The speed of the fluid flow through the 3.0-inch section will be what factor times that through the 1.0-inch section?

(1/9)

Water flows at 15 m/s through a pipe with radius 0.040 m. The pipe goes up to the second floor of the building, 3.0 m higher, and the pressure remains unchanged. What is the speed of the water flow in the pipe on the second floor?

(13 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 railroad freight car, mass 15 000 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 15 000-kg car is preserved in the two-coupled cars after collision?

(23%)

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 magnitude of the vertical velocity component of the rock as it hits the ground?

(29 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)

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 12.4 + 11 + 67.37 + 4.201?

95

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 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)

A 50-g cube of ice, initially at 0.0C, is dropped into 200 g of water in an 80-g aluminum container, both initially at 30C. What is the final equilibrium temperature? (Specific heat for aluminum is 900 J/kgC, the specific heat of water is 4 186 J/kgC, and Lf = 3.33 × 105 J/kg.)

(9.5C)

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)

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)

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 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 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 15-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.)

(0.07 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 ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water?

(0.258 N)

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 uniform pressure of 7.0 105 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 )

(0.5 * 103 %)

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 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)

An ideal fluid, of density 0.90 103 kg/m3 , flows at 6.0 m/s through a level pipe with radius of 0.50 cm. The pressure in the fluid is 1.3 105 N/m2 . This pipe connects to a second level pipe, with radius of 1.5 cm. Find the speed of flow in the second pipe.

(0.67 m/s)

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)

An automobile gas tank is filled to its capacity of 15.00 gallons with the gasoline at an initial temperature of 10C. The automobile is parked in the sun causing the gasoline's temperature to rise to 60C. 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.

(0.72 gallons)

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)

A swimming pool heater has to be able to raise the temperature of the 40 000 gallons of water in the pool by 10.0 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.)

(1 770 kWh)

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 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)

A spherical air bubble originating from a scuba diver at a depth of 18.0 m has a diameter of 1.0 cm. What will the bubble's diameter be when it reaches the surface? Assume constant temperature.

(1.4 cm)

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 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)

A 3.00-g lead bullet is traveling at a speed of 240 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)

(113C )

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 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)

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 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)

A 0.400-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?

(16.7 N)

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 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 block of wood has density 0.50 g/cm3 and mass 1 500 g. It floats in a container of oil (the oil's density is 0.75 g/cm3 ). What volume of oil does the wood displace?

(2 000 cm3 )

A cube of wood of density 0.78 g/cm3 is 10 cm on a side. When placed in water, what height of the block will float above the surface?

(2.2 cm)

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 )

I place a 500-g ice cube (initially at 0C) in a Styrofoam box with wall thickness 1.0 cm and total surface area 600 cm2 . If the air surrounding the box is at 20C and after 4 hours the ice is completely melted, what is the conductivity of the Styrofoam material? (Lf = 80 cal/g)

(2.3 * 10-4 cal/s*cm*C)

. 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 )

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)

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)

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)

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 )

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)

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 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 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 uniform bridge span weighs 50.0 103 N and is 40.0 m long. An automobile weighing 15.0 103 N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the left pier provide?

(29.5 * 103 N)

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)

How many atoms are present in a sample of pure iron with a mass of 300 g? (The atomic mass of iron = 56 and NA = 6.02 1023)

(3.2 * 1024)

A rectangular steel plate with dimensions of 30 cm 25 cm is heated from 20C to 220C. What is its change in area? (Coefficient of linear expansion for steel is 11 106 /C.)

(3.3 cm2)

What is the total force on the bottom of a 2.0-m-diameter by 1.0-m-deep round wading pool due to the weight of the air and the weight of the water? (1 atmosphere = 1.0 105 N/m2 )

(3.4 * 105 N)

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)

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)

What is the root-mean-square speed of chlorine gas molecules at a temperature of 320 K? (R = 8.31 J/molK, NA = 6.02 1023, and the molecular mass of Cl2 = 71)

(335 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)

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 temperature change from 15C to 35C corresponds to what incremental change in F?

(36)

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 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 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)

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)

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 blimp is filled with 400 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3 ; the density of helium is 0.18 kg/m3 .)

(444 kg)

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?

(49 cm/s)

What is the total mass of the Earth's atmosphere? (The radius of the Earth is 6.4 106 m, and atmospheric pressure at the surface is 105 N/m2 .)

(5 1018 kg)

A copper wire of length 2.0 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?

(5.0 mm)

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 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)

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)

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 piece of aluminum has density 2.70 g/cm3 and mass 775 g. The aluminum is submerged in a container of oil of density 0.650 g/cm3 . A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal?

(588 g)

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 62C by the solar collectors and the house is maintained at 20C? (Specific heat of rock is 0.21 cal/gC.)

(6 100 kg)

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)

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

(6.3 * 103 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 )

A 15 000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.040-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?

(600 N)

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)

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)

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 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)

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)

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)

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)

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 tank with a volume of 0.150 m3 contains 27.0C helium gas at a pressure of 100 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

(884 balloons)

. 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)

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 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 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)

Two particles collide, one of them initially being at rest. Is it possible for both particles to be at rest after the collision?

(No, momentum will not be conserved.)

An object of mass m moving at speed v0 strikes an object of mass 4m 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?

(No, the kinetic energy increased by ½ mv2 .)

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)

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

(temperature)

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)

The number 0.00017 has how many significant figures?

2

If the length of a box is educed to one-third of its original value and the width and height are doubled, by what factor has the volume changed?

3/2

The length and width of a standard sheet of paper is measured, and then the area is found by calculation to be 93.50 in2 . What is the number of significant figures in the width measurement must be at least?

4

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 )

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)

. 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?

(120 m)

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 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)

. 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)

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)

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 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)

A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F is now removed and another force F' is applied at the midpoint of the rod. If F' is at an angle of 30o with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

(4F)

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)

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)