Week 4
About 40 J is required to push a crate 4 m across a floor. If the push is in the same direction as the motion of the crate, the force on the crate is about _________.
10 N
What will the kinetic energy of a pile driver ram be if it starts from rest and undergoes a 10 kJ decrease in potential energy?
10 kJ
A machine puts out 100 watts of power for every 1,000 watts put into it. The efficiency of the machine is _________.
10%
A melon is tossed straight upward with 100 J of kinetic energy. If air resistance is negligible the melon will return to its initial level with a kinetic energy of _________.
100 J
What is the efficiency of a machine that miraculously converts all the input energy to useful output energy?
100%
A force of 50 N is applies to the end of a lever, which is moved a certain distance. If the other end of the lever moves one-third as far, how much force does it exert?
150 N
A 2-kg box of taffy candy has 40 J of potential energy relative to the ground. Its height above the ground is _________.
2 m
If you push a crate horizontally with 100 N across a 10-m factory floor and the friction between the crate and the floor is a steady 70 N, how much kinetic energy does the crate gain?
300 J
The work done in pushing a TV set a distance of 2 m with an average force of 20 N is _________.
40 J
In a simple machine, how much work is done when an input of 10 N acts over a distance of 5 m?
50 J
A motorcycle moving at 50 km/h skids 10 m with locked brakes. How far will it skid with locked brakes when traveling at 150 km/h?
90 m
A) How much work is done when you push a crate horizontally with 150 N across a 15-m factory floor? B) If the force of friction on the crate is a steady 70 N, find the KE gained by the crate. C) Find the energy turned into heat.
A) W=2300 J B) K=1200 J C) Q=1050 J
The roller coaster ride starts from rest at point A. A) Rank speed from greatest to least at each point. B) Rank KE from greatest to least at each point. C) Rank PE form greatest to least at each point.
A) d, b, c, e, a B) d, b, c, e, a C) a, e, c, b, d
No work is done by gravity on a bowling ball that is resting or moving on a bowling alley because the force of gravity on the ball acts perpendicular to the surface. But on an incline, the force of gravity has a vector component parallel to the alley, as in B. A) How does this component account for the acceleration of the ball? B) How does this component account for the work done on the ball to change its kinetic energy?
A) in accord with Newton's second law, the component of gravitational force that is parallel to the incline in B produces an acceleration parallel to the incline B) in accord with the work-energy theorem, that parallel force component multiplied by the distance the ball travels is equal to the change in the ball's kinetic energy
A) How does the lever arm change if you decrease the angle of the force? B) How does the lever arm change when you decrease the distance to the nut? C) How does the force needed to turn the wrench change if you increases the lever arm?
A) it decreases B) it decreases C) it decreases
A) Is it easier to balance a long rod with a mass attached to it when the mass is closer to your hand or when the mass is further away? B) How does the rotational inertia of the rod with the mass toward the bottom compare with the rotational inertia of the mass toward the top? C) Why does the rotational inertia of the rod with the attached mass closer to your hand compare the way it does with the rotational inertia of the the rod with the attached mass further away? D) Is it easier for a circus performer to balance a long rod held vertically with people hanging off the other end, or the same long rod without the people at the other end, and why?
A) it is easier when the mass is farther from your hand B) the rotational inertia of the rod with the mass closer to the top is greater than the rotational inertia of the rod with the mass closer to the bottom C) rotational inertia depends on whether the mass is farther or closer to the point of rotation. the farther the mass is, the higher the rotational inertia D) it is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater
A) Which word in the statement of this problem allows you to assume that the table is frictionless? B) Suppose the potential energy of the block at the table is given by mgh/3. This implies that the chosen zero level of potential energy is _________. C) If the zero level is a distance 2h/3 above the floor, what is the potential energy U of the block on the floor? D) Considering that the potential energy of the block at the table is mgh/3 and that on the floor is -2mgh/3, what is the change in potential energy ΔU of the block if it is moved from the table to the floor? E) Which most simplified form of the law of conservation of energy describes the motion of the block when it slides from the top of the table to the bottom of the ramp? F) As the block slides down the ramp, what happens to its kinetic energy K, potential energy U, and total mechanical energy E? G) Using conservation of energy, find the speed vb of the block at the bottom of the ramp. H) Which most simplified form of the law of conservation of energy describes the motion of the block as it slides on the floor from the bottom of the ramp to the moment it stops? I) As the block slides across the floor, what happens to its kinetic energy K, potential energy U, and total mechanical energy E? J) What force is responsible for the decrease in the mechanical energy of the block? K) Find the amount of energy E dissipated by friction by the time the block stops.
A) smooth B) a distance 2h/3 above the floor C) U= -2mgh/3 D) ΔU = -mgh E) 1/2mv2i+mghi=1/2mv2f+mg F) K increases; U decreases; E stays the same G) vb = √(v^2)+2gh H) 1/2mv2/i+Wnc=0 I) K decreases; U stays the same; E decreases J) friction K) E= 1/2mv^2+mgh
Consider a bob attached by a string, a simple pendulum, that swings to and fro. A) Why doesn't the tension force in the string do work on the pendulum? B) Explain, however, why the force due to gravity on the pendulum at nearly every point does do work on the pendulum. C) What is the single position of the pendulum where "no work by gravity" occurs?
A) tension in the string is everywhere perpendicular to the arc of the pendulum , with no component of tension B) in the case of gravity, a component of gravitational force on the pendulum exists parallel to the arc, which does work and changes the kinetic energy of the pendulum C) at the pendulum's lowest point
The figure below shows two blocks suspended by a single cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord's weight can be ignored. A) Which of the following statements correctly described the system shown in the figure? B) What happens when block B moves downward?
A) the angular acceleration of the pulley is nonzero B) the cord's tension on the right side of the pulley is higher than on the left side
A) What happens the first time Dr. Hewitt lifts the bowling ball near his teeth and lets go? B) Why does the bowling ball behave the way it does the first time Dr. Hewitt lifts the bowling ball near his teeth and lets go? C) What happens the second time Dr. Hewitt lifts the bowling ball near his teeth and gives it a push? D) Why does the bowling ball behave as it does when Dr. Hewitt lifts it and gives it a push?
A) the ball returns to Dr. Hewitt, stopping almost exactly at the point where it was released B) all of the initial energy of the ball was converted completely back to potential energy when the ball returned C) the ball leaves Dr. Hewitt and returns to him, going past the point where it was released D) the extra energy from the push is converted into kinetic energy, which is then converted into more potential energy at the end of the motion than the ball had when it was released
Acrobat Bart at the circus drops vertically onto the end of a see-saw, with his partner Art equidistant from the fulcrum at the other end. Art is propelled straight upward a distance twice that of Bart's dropping distance. Neglecting inefficiencies we see _________.
Art has half the mass of Bart
Select the correct equations that show that a machine that has an input of 100 J and an output of 25 J is 25% efficient.
Efficiency η=(Eout/Ein)⋅100%=((25J)/(100J))⋅100%=25%
Nellie Newton applies a force of 58 N to the end of a lever, which is moved a certain distance. If the other end of the lever moves one-third as far, find the force it exerts.
F= 170 N
In raising a 4,200-N piano with a pulley system, the workers note that for every 2.1 m of rope pulled downward, the piano rises 0.22 m. Ideally, find the force that is required to lift the piano.
F= 440 N
Belly-flop Bernie dives from atop a a tall flagpole into a swimming pool below. His potential energy at the top is 12,000 J (relative to the surface of the pool). What is his kinetic energy when his potential energy reduces to 1,000 J?
KE= 1.1x10^4 J
Calculate the kinetic energy of an 86-kg scooter moving at 12 m/s.
KE=6200 J
Select the correct equation that shows that 25 W of power is required to give a brick 100 J of PE in a time of 4 s.
P=W/t=(100 J)/(4 s)= 25 W
Select the correct equations that show the gravitational potential energy of a 1000-kg boulder raised 3 m above ground level is 30,000 J.
PE=mgh=(1000 kg) * (10 N/kg) * (3 m) = 30,000 J
Select the correct equations that show that when a 3.0-kg book is lifted 1.2 m its increase in gravitational potential energy is 36 J.
PE=mgh=(3.0 kg) * (10 m/s^2) * (1/2 m) = 36 J
In the hydraulic machine shown, you observe that when the small piston is pushed down 10 cm, the large piston is raised 1 cm. If the small piston is pushed down with a force of 100 N, what is the most weight that the large piston can support?
W= 1,000 N
The second floor of a house is 6 m above the street level. How much work is required to lift a 300-kg refrigerator to the second-story level?
W=1.8x10^4 J
Calculate the work done when a 26-N force pushes a cart 4.0 m.
W=100 J
Select the correct equations that show that 9.6 J of work is done when a force of 8.0 N moves a book 1.2 m.
W=F*d=(8.0 N) * (1.2 m) = 9.6 J
Select the correct equations that show that 64 J of work is done when a 8.0-kg block of ice is moved from rest to a speed of 4.0 m/s.
W=mv^2/2=((8.0 kg) * (4.0 m/s^2)/2= 64 J
The bob of a simple pendulum has its maximum kinetic energy at the _________.
bottom of its swing
When traveling twice as fast your kinetic energy is increased _________.
by a factor of four
Energy cannot be _________.
destroyed
If a machine multiplies force by a factor of 4, what other quantity is diminished, and by how much?
distance is diminished to one-quarter
Exactly what is it that enables an object to do work?
energy
The torque exerted by a crowbar on an object increases with increased _________.
force and leverage distance
Can a machine multiply input force? Input distance? Input energy?
force: yes distance: yes energy: no
When you lift twice the load twice as high, in half the time, the increase in potential energy is _________.
four times
The work that is done when twice the load is lifted twice the distance is _________.
four times as much
An apple hanging from a limb has potential energy because of its height. If it falls, what becomes of this energy just before it hits the ground? When it hits the ground?
immediately before hitting the ground the apple's energy is kinetic energy; when it hits the ground, its energy becomes thermal energy
Consider a satellite in a circular orbit above Earth's surface. The force of gravity changes only the direction of motion of a satellite in circular motion (and keeps it in a circle); it does NOT change the satellite's speed. Work done on the satellite by the gravitational force is zero. What is your explanation?
in circular orbit, the force of gravity is everywhere perpendicular to the satellite's motion. with no component of force parallel to its motion, no work is done and its kinetic energy remains constant
Rotational inertia about the midpoint of an object becomes greater with _________.
increased mass and increased distance to mass concentration
When the speed of a moving car is doubled, how much more kinetic energy does it have?
it has four times as much
As distance increases between most of the mass of an object and its center of rotation, how does rotational inertia change?
it increases
Compared with a car moving at some original speed, how much work must the brakes of a car supply to stop a car that is moving twice as fast? How will the stopping distances compare?
it takes four times the work and four times the stopping distance
Suppose our experimenter repeats his experiment on a planet more massive than Earth, where the acceleration due to gravity is g= 30 m/s^2. When he releases the ball from chin height without giving it a push, how will the ball's behavior differ from its behavior on Earth? Ignore friction and air resistance.
it will take less time to return to the point from which it was released
A car is raised a certain distance in a service-station lift, thus giving it potential energy relative to the floor. If it were raised twice as high, how much more potential energy would it have?
it would have twice as much potential energy
What is the unit of work?
joule
If both sacks in the preceding question are lifted their respective distances in the same time, how does the power required for each compare? How about for the case in which the lighter sack is moved the same distance in half the time?
lifted in the same time, the power is the same. the light sack moving in half the time requires double the power
What are the units of measurement for tangential speed? For rotational speed?
m/s for tangential, RPM for rotational
How is a flywheel constructed to maximize its rotational inertia?
most of the mass is concentrated far from the axis
Can we correctly say that hydrogen is a new source of energy? Why or why not?
no, it takes energy to make hydrogen
Which energy production method does not ultimately depend on the Sun?
nuclear fission
What is the ultimate source of geothermal energy?
nuclear power in Earth's interior
What is recycled energy?
reused energy that otherwise would be wasted
How does speed affect the friction between a road and a skidding tire?
speed has no effect on the friction
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
tangential speed increases with distance; rotational speed is constant
Fossil fuels, hydroelectric power, and wind power ultimately get their energy from _________.
the Sun
What is the ultimate source of the energy from fossil fuels, dams, and windmills?
the Sun
A ball rolling down an incline has its maximum kinetic energy at _________.
the bottom
Two cars are raised to the same elevation on service-station lifts. If one car is twice as massive as the other, compare their gains of potential energy.
the car with twice the mass has twice the gain of potential energy
Inertia depends on mass; rotational inertia depends on mass and something else. What?
the distribution of mass about the axis of rotation
When one does twice the work in twice the time, the power expended is _________.
the same
After rolling halfway down an incline, a marble's kinetic energy is _________.
the same as its potential energy
Which will have the greater acceleration rolling down an incline: a hoop or a solid disk? Why?
the solid disk will because the mass is closer to the axis of rotation
How does the tapered rim of a wheel on a railroad allow one part of the rim to have a greater tangential speed than another part when it is rolling on a track?
the tangential speed is proportional to the radius the inside of the wheel rolls on a larger radius than the outside of the wheel
A tapered cup rolled on a flat surface makes a circular path. What does this tell you about the tangential speed of the rim of the wide end of the cup compared with that of the rim of the narrow end?
the tangential speed of the wide end is faster
A ball rolling down an incline has its maximum potential energy at _________.
the top
What is the source of energy in sunshine?
thermonuclear fusion energy
A crate of grapes lifted 10 meters gains 200 J of potential energy. If the same crate is instead lifted 20 meters, its gain in potential energy is _________.
twice as much
The work you do when pushing a shopping cart twice as far while applying the same force is _________.
twice as much
Recycled energy is mainly _________.
use of energy otherwise wasted
Emily holds a banana of mass m over the edge of a bridge of height h. She drops the banana and it falls to the river below. Use conservation of energy to find the speed of the banana just before hitting the water.
v= √2gh
When is the potential energy of something significant?
when the potential energy changes
A force sets an object in motion. When the force is multiplied by the time of its application, we call the quantity impulse, and an impulse changes the momentum of that object. What do we call the quantity force multiplied by distance?
work
How much work is done on a satellite in a circular orbit about Earth?
zero
A circus diver drops from a high pole into water far below. When he is halfway down _________.
(he has gained an amount of kinetic energy equal to half his initial potential energy, his potential energy is halved, his kinetic energy and potential energy are equal) all of the above
A light aluminum ball and a heavy lead ball of the same size roll down an incline. When they are halfway down the incline, they will have identical _________.
(momentum, potential energies, inertias, kinetic energies) none of the above
A hydraulic jack is used to lift objects such as automobiles. If the input force is 200 N over a distance of 1 meter, the output force over a distance of 0.1 meter is ideally _________.
2,000 N
A hydraulic press has its input piston depressed 20 centimeters while the output piston is raised 1 centimeter. A 1-newton input can lift a load of _________.
20 N
A jack system will increase the potential energy of a heavy load by 1,000 J with a work input of 2,000 J. The efficiency of the jack system is _________.
50%
When the useful energy output of a simple machine is 100 J, and the total energy input is 200 J, the efficiency is _________.
50%
If an input of 100 J in a pulley system increases the potential energy of a load by 60 J, what is the efficiency of the system?
60%
A) Calculate the work done in lifting a 460-N barbell 1.6 m above the floor. B) What is the gain of the potential energy of the barbell when it is lifted to this height?
A) W= 740 J B) ΔU = 740 J
A) Two identical cars are driving in opposite directions at the same speed. Their kinetic energies have _________. B) A motorcycle drives up a steeply inclined ramp. The work done on the motorcycle by Earth's gravitational force is _________. C) During a certain time interval, the net work done on an object is zero joules. We can be certain that _________. D) The amount of kinetic energy an object has depends on its mass and its speed. Rank the following sets of oranges and cantaloupes from least kinetic energy to greatest kinetic energy.
A) the same magnitude and sign B) negative C) the object's final speed was the same as its initial speed D) mass: 4m speed: 1/4 v; total mass: 2 m speed: 1/2 v; mass: m speed: v; total mass: 4 m speed: v & mass: 4m speed: v
A) Where on the track is the skater's kinetic energy the greatest? B) As the skater is skating back and forth, where does the skater have the most potential energy? C) Observe the total energy bar on the Bar Graph. As the skater is skating back and forth, which statement best describes the total energy? D) Match the approximate numerical values on the left with the energy type categories on the right to complete the equations. Assume that the mass of the skater is 75 kg and that the acceleration of gravity is 9.8 N/kg. E) Based on the previous question, which statement is true? F) If the skater started from rest 4 m above the ground (instead of 7m), what would be the kinetic energy at the bottom of the ramp (which is still 1 m above the ground)? G) Consider again the case where the skater starts 7 m above the ground and skates down the track. What is the skater's speed when the skater is at the bottom of the track? H) When the skater starts 7 m above the ground, how does the speed of the skater at the bottom of the track compare to the speed of the skater at the bottom when the skater starts 4 m above the ground? I) If the skater starts from rest at position 1, rank, in increasing order from least to greatest, the kinetic energy of the skater at the five positions shown.
A) the skater's kinetic energy is ... at its maximum value at the lowest point of the track B) the skater's potential energy is ... at its maximum value at the locations where the skater turns and goes back in the opposite direction C) the total energy is ... the same at all locations of the track D) total energy at initial position= 5145 J potential energy at initial position= 5145 J kinetic energy at initial position = 0 J total energy at bottom of track = 5145 J potential energy at bottom of track= 735 J kinetic energy at bottom of track = 4410 J E) the kinetic energy at the bottom of the ramp is ... equal to the amount of potential energy loss in going from the initial location to the bottom F) 2205 J G) 11 m/s H) the speed is ... higher, but less than twice as fast I) 1, 3, 5&2, 4
Consider three axes of rotation for a pencil: along the lead, at right angles to the lead at the middle, and at right angles to the lead at one end. Rate the rotational inertias about each axis from smallest to largest.
axis along the head, through the center, through one end
Why does bending your legs when running enable you to swing your legs to and fro more rapidly?
bending your legs shortens them, thus reducing rotational inertia
Which requires more work: lifting a 50-kg sack a vertical distance of 2 m or lifting a 25-kg sack a vertical distance of 4 m?
both take the same 1000 J
Two identical golf carts move at different speeds. The faster cart has twice the speed and therefore has _________.
four times the kinetic energy
The tangential speed on the outer edge of a rotating carousel is _________.
greater than toward the center
Consider an ideal pulley system. If you pull one end of the rope 0.60 m downward with a 46-N force, find the height you can lift a 230-N load.
h= 0.12 m
A block of ice sliding down an incline has half its maximum kinetic energy _________.
halfway down
When Joshua brakes his speeding bicycle to a stop, kinetic energy is transformed to _________.
heat
Which is easier to get swinging: a baseball bat held at the narrow end or a bat held closer to the massive end (choked up)? Also answer for a short bat versus a long bat.
the easiest is choked up and a short bat
No work is done by gravity on a bowling ball that rolls along a bowling alley because _________.
the force on the ball is at right angles to the ball's motion
