Physics Exam 4
At what speed do a bicycle and its rider, with a combined mass of 100 kgkg, have the same momentum as a 1500 kgkg car traveling at 1.6 m/sm/s ? Express your answer with the appropriate units.
( 1500 x 1.6 )/ 100 = 24m/s
As part of a safety investigation, two 1600 kgkg cars traveling at 22 m/sm/s are crashed into different barriers. Find the average force exerted on the car that hits a concrete barrier and takes 0.16 ss to stop. Express your answer with the appropriate units.
(-1600x22) / 0.16 =220,000
As part of a safety investigation, two 1600 kgkg cars traveling at 22 m/sm/s are crashed into different barriers. Find the average force exerted on the car that hits a line of water barrels and takes 1.6 ss to stop. Express your answer with the appropriate units.
(-1600x22) / 1.6 = 35200/1.6 = 22,000N
A student throws a 130 gg snowball at 8.5 m/sm/s at the side of the schoolhouse, where it hits and sticks. What is the magnitude of the average force on the wall if the duration of the collision is 0.18 ss ?
.130x8.5 = x x/0.18 = 6.1N
In principle, when you fire a rifle, the recoil should push you backward. How big a push will it give? Let's find out by doing a calculation in a very artificial situation. Suppose a man standing on frictionless ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kgkg, and the mass of the bullet is 10 gg. If the bullet leaves the muzzle at a speed of 500 m/sm/s, what is the final speed of the man?
0.01x500/70 =0.07142m/s
Climbing ropes stretch when they catch a falling climber, thus increasing the time it takes the climber to come to rest and reducing the force on the climber. In one standardized test of ropes, an 80 kgkg mass falls 4.8 mm before being caught by a 2.5-mm-long rope.
0.0705s
What is the minimum work done by the heart to pump 290 gg of blood from a person's foot to his heart 1.5 mm away? Use gg = 10 m/s2m/s2.
0.29 x 10 x 1.5 = 4.35J
How much work must you do to push a 12 kgkg block of steel across a steel table at a steady speed of 1.2 m/sm/s for 5.8 ss ? The coefficient of kinetic friction for steel on steel is 0.60. Express your answer in joules.
0.60 x 12 x 9.8 = 70.56N deltax = 5.8 x 1.2 = 6.96 6.96 x 70.56 x 1 =490J
A dog can provide sufficient power to pull a sled with a 60 NN force at a steady 2.0 m/sm/s. Suppose the dog is hitched to a different sled that requires 120 NN to move at a constant speed. How fast can the dog pull this second sled?
1.0m/s
Sam's job at the amusement park is to slow down and bring to a stop the boats in the log ride. If a boat and its riders have a mass of 1100 kgkg and the boat drifts in at 1.5 m/sm/s how much work does Sam do to stop it?
1.5^2 x 1100 x 1/2= -1237.5J
A 1.6 kg book is lying on a 0.76 mm -high table. You pick it up and place it on a bookshelf 2.2 mm above the floor. During this process, how much work does gravity do on the book? Express your answer with the appropriate units.
1.6 x 9.81 x (2.2-0.76) = -22.60J
How much energy can be stored in a spring with kkk = 480 N/m if the maximum possible stretch is 18 cmcm ? Express your answer in joules.
1/2 x 480 x 0.18^2 = 7.8
The world's fastest humans can reach speeds of about 11 m/sm/s. In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?
11^2 / 2x9.8 = 6.17m
Divers change their body position in midair while rotating about their center of mass. In one dive, the diver leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of inertia of the diver in a straight position is 14 kg⋅m2kg⋅m2 and in a tucked position is 4.0 kg⋅m2kg⋅m2, by what factor does her angular speed increase?
14/4 = 3.5
Mark pushes his broken car 160 mm down the block to his friend's house. He has to exert a 140 NN horizontal force to push the car at a constant speed. How much thermal energy is created in the tires and road during this short trip? Express your answer with the appropriate units.
160x140=22400 22.4kJ
If Luis pulls straight down on the end of a wrench that is tilted θθ = 30∘∘ above the horizontal and is rrr = 35 cmcm long, what force must he apply to exert a torque of -17 N⋅mN⋅m ?
17N-M / .35 = 48.57 N Tangential Force 48.57 / COS 30 deg (.866) = 56 Newtons (answer)
A crate slides down a ramp that makes a 20∘∘ angle with the ground. To keep the crate moving at a steady speed, Paige pushes back on it with a 72 NN horizontal force. How much work does Paige do on the crate as it slides 4.0 mm down the ramp?
180-20 = 160 W = 72x4.0xcos160 = -270.6J
Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates with constant speed 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. What is the magnitude of the angular acceleration of the salad spinner as it slows down?
20.0rev / 5.00s = 4.00rev / s(2πrad / rev) = 25.1rad / s ω² = ω₀² + 2αΔθ α = (ω² - ω₀²) / 2Δθ = [(25.1rad/s)² - 0] / (2 x 37.7rad) = 8.36rad/s²
Specifications require the oil filter for your car to be tightened with a torque of 30 N⋅mN⋅m. You are using a 15-cmcm-long oil filter wrench, and you apply a force at the very end of the wrench in the direction that produces maximum torque. How much force should you apply?
200 N
A 1.6 kg book is lying on a 0.76 mm -high table. You pick it up and place it on a bookshelf 2.2 mm above the floor.During this process, how much work does your hand do on the book? During this process, how much work does your hand do on the book?
22.60J
A child on a merry-go-round takes 3.3 ss to go around once. What is his angular displacement during a 1.0 ss time interval? Express your answer in radians.
2pi/3.3
A Ferris wheel on a California pier is 27 mm high and rotates once every 32 seconds in the counterclockwise direction. When the wheel starts turning, you are at the very top. What is your angular position 75 seconds after the wheel starts turning, measured counterclockwise from the top? Express your answer as an angle between 0∘∘ and 360∘∘. Express your answer in degrees.
32 seconds to turn 360º or 360/32 = 11.25º/s 11.25º/s x 75s = 843.75º subtract 360 twice to get 123.75º, rounded to 124º
What is your power output while doing so? Express your answer in watts.
490/5.8 = 84.67W
The lightweight wheel on a road bike has a moment of inertia of 0.097 kg⋅m2kg⋅m2. A mechanic, checking the alignment of the wheel, gives it a quick spin; it completes 5 rotations in 2.2 ss. To bring the wheel to rest, the mechanic gently applies the disk brakes, which squeeze pads against a metal disk connected to the wheel. The pads touch the disk 7.1 cmcm from the axle, and the wheel slows down and stops in 1.4 ss. What is the magnitude of the friction force on the disk? Express your answer with the appropriate units.
5x2xpi / 2.2 = w Fx(7.1x10^-2)x1.4 = 0.097xw Fx1.26876 = 0.097xw F=13.935N
A billiard ball of mass 0.28 kgkg hits a second, identical ball at a speed of 7.9 m/sm/s and comes to rest as the second ball flies off. The collision takes 250 μsμs. What is the average force on the second ball?
8848N
WW is the work done on the system, and KK, UU, and EthEth are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. Select a specific example of a system with the energy transformation shown.K→ΔEth
A wood block sliding across a rough horizontal surface and slowing to a stop.
WW is the work done on the system, and KK, UU, and Eth are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. Select a specific example of a system with the energy transformation shown.U→ΔEth Select a specific example of a system with the energy transformation shown.
A wood block sliding down a rough inclined surface at a constant speed.
In which situation listed would angular acceleration be positive?
An object is rotating counter-clockwise and speeding up.
For an extended object, the weight force can be considered to act at which point?
At the center of gravity of the object
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A and Bobby is riding at point B. Who has the greater magnitude of centripetal acceleration?
Bobby has the greater magnitude of centripetal acceleration.
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A and Bobby is riding at point B. Which child moves with greater magnitude of linear velocity?
Bobby has the greater magnitude of linear velocity.
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A and Bobby is riding at point B. Who moves with greater magnitude of angular acceleration?
Both Ana and Bobby have the same magnitude of angular acceleration.
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A and Bobby is riding at point B. Who moves with greater magnitude of angular velocity?
Both Ana and Bobby have the same magnitude of angular velocity.
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A and Bobby is riding at point B. Who moves with greater magnitude of tangential acceleration?
Both Ana and Bobby have the same magnitude of tangential acceleration.
A nut needs to be tightened with a wrench. Which force shown in the figure will apply the greatest torque to the nut?
C
A driver holds his hands on opposite sides of the 35-cmcm-diameter steering wheel in a modern sports car. A torque of 4.5 N⋅mN⋅m is required to turn the wheel. If the driver applies an equal force on each side of the wheel, what is the minimum force each hand must supply?
F = T/d = 4.5/0.35 = 12.9 N
A billiard ball of mass 0.28 kgkg hits a second, identical ball at a speed of 7.9 m/sm/s and comes to rest as the second ball flies off. The collision takes 250 μsμs. What is the average force on the first ball?
F=0.28 x (0-7.9)/(0.00025) =-8848N
In a Little League baseball game, a 145 gg ball enters the strike zone with a speed of 15.0 m/sm/s . The batter hits the ball, and it leaves his bat with a speed of 23.0 m/sm/s in exactly the opposite direction.If the bat is in contact with the ball for 1.4 msms , what is the magnitude of the average force exerted by the bat on the ball?
F=5.51/1.4E-3 =3935.7
How does a car's kinetic energy change when it speeds up from 10 to 20 m/s?
It quadruples.
In a Little League baseball game, a 145 gg ball enters the strike zone with a speed of 15.0 m/sm/s . The batter hits the ball, and it leaves his bat with a speed of 23.0 m/sm/s in exactly the opposite direction. What is the magnitude of the impulse delivered by the bat to the ball?
J = 0.145 x (-23-15) = 5.51 N*s
An object's angular momentum is proportional to its __________.
Moment of Inertia
The torque needed to open a factory-sealed jar is about the same as the torque required to turn the wheel on a passenger car. You know that the force necessary to turn your car's steering wheel is less than the force needed to open a jar.
Product of the force and the moment arm, Greater
A bicycle rim has a diameter of 0.65 mm and a moment of inertia, measured about its center, of 0.23 kg⋅m2kg⋅m2 . What is the mass of the rim? Express your answer with the appropriate units.
R=0.65/2 = 0.325m I=0.23 M=I/R^2 =0.23/0.325^2 = 2.1775kg or 2.2
A 60 kg runner in a sprint moves at 11 m/sm/s. A 60 kg cheetah in a sprint moves at 33 m/s. By what factor does the kinetic energy of the cheetah exceed that of the human runner?
Runner 1/2 x 60 x 11^2=3630 Cheetah 1/2 x 60 x 33^2=32670 answer = 9
If you grasp a hammer by its lightweight handle and wave it back and forth, and then grasp it by its much heavier head and wave it back and forth, as in the (Figure 1), you'll find that you can wave the hammer much more rapidly in the second case, when you grasp it by the head.
Smaller, easier, farther from
Five forces are applied to a door, as seen from above in
Ta and Tc = positive Tb and Td = negative Te = zero
Your car's engine is a heat engine; it converts the thermal energy from burning fuel into energy to move your car and power its systems. On a cold winter day, you needn't feel guilty about cranking up the heat in your car; running the heater doesn't cost any additional energy beyond the small amount needed to run the fan. Why is this so?
The heater uses inevitable waste heat from the car's engine.
You are bowling with a 10-pound ball that you throw at 10 mphmph, and you've decided that you need to hit the pins with a ball that has more momentum. What are two possible changes you could make?
Throw a ball with a greater mass or increase the throw speed.
You are pulling a child in a wagon. The rope handle is inclined upward at a 60∘∘ angle. The tension in the handle is 20 NN. How much work do you do if you pull the wagon 160 mm at a constant speed?
W = 20 x 160 x cos60 = 1600J
To throw the discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discus after making one complete revolution. The diameter of the circle in which the discus moves is about 1.8 mm . If the thrower takes 1.1 ss to complete one revolution, starting from rest, what will be the speed of the discus at release?
a = 2(pi) / (1.1/2) a= 11.424 r= 1.8/2 = 0.9 0.9 x 11.424 =10.28m/s
When your hands are cold, you can rub them together to warm them.
chemical, chemical, kinetic, kinetic, thermal
A Ferris wheel on a California pier is 27 mm high and rotates once every 32 seconds in the counterclockwise direction. When the wheel starts turning, you are at the very top. What is your speed vv?
circumference = πD = 27π m speed = 1 rev/32s = 27π m / 32s = 2.65 m/s
If you raise an object to a greater height, you are definitely increasing its __________.
gravitational potential energy
The total momentum of a system is conserved __________.
if no external forces act on the system
If a system is isolated, the total energy of the system ________.
is constant
While standing still on a basketball court, you throw the ball to a teammate. Why do you not move backward as a result? Is the law of conservation of momentum violated? Drag the terms on the left to the appropriate blanks on the right to complete the sentences. ResetHelp gravity force of the Earth on your body friction force of the floor on your feet is is not
is not, is not, friction force of the floor on your feet.
The units of linear momentum are _________.
kg·m/s
In an inelastic collision,
momentum is conserved
When you catch a water balloon, it's best to start with your hand in motion, moving with the balloon, and then gradually slow it to rest.
momentum, force, p=Ft, with the balloon, larger, smaller, momentum
If an object is rotating clockwise, this corresponds to a _____ angular velocity.
negative
What is the angular speed of the tip of the minute hand on a clock, in rad/s? Express your answer in radians per second to three significant figures.
pi/1800
The angular displacement of a rotating object is measured in _____.
radians
You drop two balls from a tower, one of mass mm and the other of mass 2m2m. Just before they hit the ground, which ball, if either, has the larger kinetic energy? Just before they hit the ground, which ball, if either, has the larger kinetic energy?
second
At what speed does a 1600 kg compact car have the same kinetic energy as a 18000 kg truck going 24 km/h ? Express your answer in kilometers per hour.
sqrt(18000x24^2 / 1600) =80.5km/h
How far must you stretch a spring with kkk = 1600 N/m to store 260 JJ of energy? Express your answer in meters.
sqrt(2x260 / 1600) = 0.57m
Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates with constant speed 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. How long does it take for the salad spinner to come to rest?
t=25.1/-8.38 = 3.0s
A net torque applied to an object causes __________.
the angular velocity of the object to change
Which factor does the torque on an object NOT depend on?
the objects angular velocity
Moment of inertia is __________.
the rotational equivalent of mass
A small grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2kg⋅m2 . What net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2rad/s2 ? Express your answer in newton-meters.
we know net torque = 4.0x10^-5 x 150 = 6x10^-3N-m
Which of the following is an energy transfer?
work
