PHYS 1210 Ch. 7 Energy
What happens to the force of attraction between two planets when the masses of both are doubled?
-The force increases by 16. -The force doubles. >The force quadruples. -The force remains the same.
An object that has kinetic energy must be
-at rest. -at an elevated position. >moving. -falling. -none of these
A weight watcher who normally weighs 400 N stands on top of a very tall ladder so she is one Earth radius above Earth's surface. How much is her weight there?
>100 N -400 N -0 -200 N -none of the above
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. -It would have the exact same potential energy. -It would have equal and opposite potential energy. -It would have half as much potential energy.
What happens to the force of attraction between two planets when the distance between them is doubled?
>The force decreases to one quarter. -The force doubles. -The force remains the same. -The force decreases to half.
A physics instructor demonstrates energy conservation by releasing a heavy pendulum bob, as shown in the sketch, allowing it to swing to and fro. What would happen if, in his exuberance, he gave the bob a slight shove as it left his nose? Explain.
If the bob starts with the shove from the professor then its total energy is more than what it would be if it wasn't pushed and started from zero. It will have a greater speed due to the push and that extra energy will smash the exuberant physicist in the nose.
Why is it easier to stop a lightly loaded truck than a heavier one that has equal speed?
It is easier to stop a lightly loaded truck than a heavier one moving at the same speed because it has less KE and will therefore require less work to stop. (An answer in terms of impulse and momentum is also acceptable.)
Part A Is gravitational force acting on a person who falls off a cliff? Part B Is gravitational force acting on an astronaut inside an orbiting space shuttle?
Part A >yes -no Part B >yes -no
Part A How many joules of potential energy does a 1.5-kg book gain when it is elevated 4.0 m ? Part B When it is elevated 8.0 m ? *Gravitational potential energy = weight × height: PE = mgh
Part A ΔPE = 59 J Part B ΔPE = 120 J *Actual is 118 but round to 2 SF
What would be the path of the Moon if somehow all gravitational forces on it vanished to zero?
Without a force acting on the Moon it would continue on a straight path with constant velocity according to Newton's 1st Law.
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?
• When an apple falls from a tree, all its PE is converted to KE just before it hits the ground. • After it hits, some energy will be transformed to heat, some to deformation & some remains as KE as the apple bounces off the ground.
The ball rolling down an incline has its maximum potential energy at
-halfway down. >the top. -a quarter of the way down. -the bottom.
After rolling halfway down an incline, a marble's kinetic energy is
-less than its potential energy. >the same as its potential energy. -greater than its potential energy. -impossible to determine.
A heavy and a light object released from the same height in a vacuum have equal
-momenta. -weights. >accelerations. -kinetic energies. -none of the above
change in the kinetic energy is equal to the negative of the change in the potential energy:
K2−K1=−(U2−U1), or ΔK1=−ΔU2
It takes 40 J to push a large box 4 m across a floor. Assuming the push is in the same direction as the move, what is the magnitude of the force on the box?
-40 N >10 N -160 N -4 N -none of these
When an object is in motion, which of the following could not have a value of zero?
-velocity -mass -kinetic energy -inertia >None of the above could be zero.
What do we call the gravitational force between Earth and your body?
Weight
Part A Click on the Energy vs. Position button, and de-select all forms of energy except kinetic energy. Where on the track is the skater's kinetic energy the greatest? *The kinetic energy of an object is given by K=(1/2)mv2, where v is the speed of the object and m is the mass of the object. Thus, the skater's kinetic energy is greatest at the lowest point of the track, where the skater is moving the fastest. Part B Change the Energy vs. Position graph to display only potential energy. As the skater is skating back and forth, where does the skater have the most potential energy? *The gravitational potential energy of an object is given by U=mgy, where y is the object's height above the potential energy reference, which is currently the ground. Thus, the skater's potential energy is greatest at the locations where the skater turns to go back in the opposite direction, where the skater is the highest above the reference line. Notice that the skater's potential energy is greatest where the kinetic energy is the lowest, and vice versa. Part C Because we are ignoring friction, no thermal energy is generated and the total energy is the mechanical energy, the kinetic energy plus the potential energy: E=K+U. Display the total energy in the Energy vs. Position graph. As the skater is skating back and forth, which statement best describes the total energy? *The mechanical energy (kinetic plus potential) is conserved. (Since there is no friction, the mechanical energy is equal to the total energy.) When the kinetic energy is relatively small, the potential energy is relatively large, and vice versa. Part D Ignoring friction, the total energy of the skater is conserved. This means that the kinetic plus potential energy at one location, say E1=K1+U1, must be equal to the kinetic plus potential energy at a different location, say E2=K2+U2. This is the principle of conservation of energy and can be expressed as E1=E2. Since the energy is conserved, the change in the kinetic energy is equal to the negative of the change in the potential energy: K2−K1=−(U2−U1), or ΔK1=−ΔU2. Select the Show Grid option. Then, pull the bottom of the track down such that it is 1 m above the ground (click and drag on the blue circle on the bottom of the track). Confirm that the mass of the skater is set to 75.0 kg (select Choose Skater to view mass) and that the acceleration of gravity is set at 9.81 N/kg . Clear all plots, place the skater on the track 7 m above the ground, and look at the resulting motion and the graph showing the energetics. Match the approximate numerical values on the left with the energy type categories on the right to complete the equations. Drag the appropriate numerical values to their respective targets. Part E Based on the previous question, which statement is true? *Because the total energy is conserved, the kinetic energy at the bottom of the hill plus the potential energy at the bottom of the hill must equal the initial potential energy (since the initial kinetic energy is zero): Kbottom+Ubottom=Uinitial. Solving for the kinetic energy, we get Kbottom=Uinitial−Ubottom, or Kbottom=5145 J−735 J=4410 J. More generally, the change in the kinetic energy is equal to the negative of the change in the potential energy. Part 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)? Part G One common application of conservation of energy in mechanics is to determine the speed of an object. Although the simulation doesn't give the skater's speed, you can calculate it because the skater's kinetic energy is known at any location on the track. 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? Express your answer numerically in meters per second to two significant figures. Part 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? Part I Change the potential energy reference line to be 7 m above the ground (select the Potential Energy Reference option, and click and drag on the dashed blue horizontal line to the 7 m grid line). Place the skater on the track 7 m above the ground, and let the skater go. Part J At the bottom of the hill, how does the kinetic energy compare to the case when the potential energy reference was the ground and the skater was released 7m above the ground? *The kinetic energy at the bottom of the track is equal to the amount of potential energy lost in going from the initial position to the bottom. Even though the total energy and initial potential energy are different from when the reference was the ground, the skater still loses the same amount of potential energy in going from 7 m down to the bottom of the track. Thus, when applying conservation of energy, any potential energy reference can be used! Part K Click Tracks in the upper-left corner of the window, and select Double Well (Roller Coaster). Then, click and drag on the blue circles to stretch and/or bend the track to make it look like that shown below.
Part A The skater's kinetic energy is; -at its maximum value at the locations where the skater turns and goes back in the opposite direction. >at its maximum value at the lowest point of the track. -the same everywhere. Part 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. -the same everywhere. -at its maximum value at the lowest point of the track. Part C The total energy is: -greatest at the locations where the skater turns and goes back in the opposite direction and smallest at the lowest point of the track. >the same at all locations of the track. -smallest at the locations where the skater turns to go back in the opposite direction and greatest at the lowest point of the track Part D 1) Total Energy at Initial Position= 5145 J 2) Potential Energy at Initial Position= 5145 J 3)Kinetic Energy at Initial Position= 0 J 4) Total Energy at Bottom of Track= 5145 J 5) Potential Energy at Bottom of Track= 735 J 6) Kinetic Energy of Bottom of Track= 4410 J Part E The kinetic energy at the bottom of the ramp is: -equal to the initial potential energy. >equal to the amount of potential energy loss in going from the initial location to the bottom. -equal to the total energy. Part F -735 J >2205 J -4410 J -2940 J Part G 11 m/s *For a 75-kg object having approximately 4410 J of energy, the speed must be roughly 11 m/s. Part H The speed is: >higher, but less than twice as fast. -the same. -four times as fast. -twice as fast. *The person will have twice as much kinetic energy. Because kinetic energy is proportional to the speed squared, the ratio of the speeds is equal to the square root of the ratio of the kinetic energies. In this case, since the ratio of the kinetic energies is 2, the ratio of the speeds is equal to the square root of 2, or roughly 1.4. Part I The total energy of the skater is: >equal to zero. -less than zero. -greater than zero. *Initially, the kinetic energy is zero because the skater is at rest and the potential energy is zero because the skater is starting at the potential energy reference line. Because energy is conserved, the skater's total energy remains zero. Part J The kinetic energy is: -greater than the case when the potential energy reference was the ground. >the same as the case when the potential energy reference was the ground. -less than the case when the potential energy reference was the ground. Part K 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. Rank from smallest to largest. To rank items as equivalent, overlap them. 1 - 3 - 2&5 - 4
When a jumbo jet slows and descends on approach to landing, there is a decrease in both its kinetic and potential energy. Where does this energy go?
The energy goes mostly into frictional heating of the air.
Somewhere between Earth and the Moon, gravity from these two bodies on a space pod would cancel. Is this location nearer Earth or the Moon?
The location near the Moon because it has a lesser mass than the Earth therefore it would have less pull on the pod if the distance were equal.
Calculate the work done when a force of 1.2 N moves a book 1.9 m . *Work = force × distance: W=Fd (remember that 1N*m = 1J)
W = 2.3 J
What is the magnitude of the gravitational force between Earth and a 1-kg body?
Weight = mg = 1 kg(10 m/s/s)= 10 newtons.
Which pulls on the oceans of Earth with a greater force?
-Moon >Sun -both pull the same.
A block of ice sliding down an incline has its maximum speed at
-the top. >the bottom. -halfway down. -difficult to predict without knowing the slope of the incline -difficult to predict without knowing the coefficient of friction
When you step on a weighing scale at noon, Earth pulls you downward and the overhead Sun pulls you upward. The reason the Sun's pull doesn't decrease your weight at noon is because
-the weighing scale is calibrated only in Earth weight. -the Sun's pull is cancelled by the gravitation of other celestial bodies. >you, the scale, and Earth are in free fall (in orbit) around the Sun. -the Sun's pull on you is negligibly small. -of tidal effects in the "solid" Earth.
A melon is projected into the air with 100 J of kinetic energy in the presence of air resistance. When it returns to its initial level its kinetic energy is
>less than 100 J. -100 J. -more than 100 J. -need more information
If you push an object twice as far while applying the same force, you do
>twice as much work. -the same amount of work. -half as much work. -four times as much work.
In the absence of air resistance, a ball thrown vertically upward with a certain initial KE will return to its original level with the same KE. When air resistance is a factor affecting the ball, will it return to its original level with the same, less, or more KE? Does your answer contradict the law of energy conservation?
It will return with less KE because of the air resistance. No It does not because the law of energy conservation says energy is transformed and never destroyed. It just loses energy the energy doesn't disappear.
Part A Calculate the force of gravity between a newborn baby of mass 3.2 kg and the obstetrician of mass 100 kg, who is 0.50 m from the baby. Given: G = 6.67 * 10^(-11) Nm^2/kg^2 Express your answer to two significant figures and include the appropriate units. Part B Which exerts more gravitational force on the baby, Mars or the obstetrician?
Part A Part B Mars >the obstetrician
If the Moon pulls Earth as strongly as Earth pulls the Moon, why doesn't Earth rotate around the Moon, or why don't both rotate around a point midway between them?
Since the moons mass is smaller than Earth's, and their rotation has to have a center point.
On a playground slide, a child has potential energy that decreases by 1000 J while her kinetic energy increases by 900 J. What other form of energy is involved, and how much?
The 100 J of potential energy that doesn't go into increasing her kinetic energy goes into thermal energy—heating her bottom and the slide.
The second floor of a house is 6 m above the street level. How much work is required to lift a 260-kg refrigerator to the second-story level?
W = 1.5×104 J *15.3kJ (=1.53×104 J) Work = 260kg × 9.81N/kg × 6 m = 15.3036kNm = 15.3kJoules
An apple falls because of the gravitational attraction to Earth. How does the gravitational attraction of Earth to the apple compare? (Apply Newton's 3rd law. Also, does force change when you interchange m1 and m2 in the equation for gravity, such that it is written as m2m1 instead of m1m2?)
~According to Newton's 3rd Law the gravitational attraction of the apples "weight" on the Earth is the same gravitational attraction that the Earth has on the apple. When one force is against the other they placed the same force on the opposing object. (Earth:apple). ~The gravitational attraction will remain the same but since Earth has more mass than the apple the apple will accelerate faster than Earth.
A 2 kg mass has 40 J of potential energy with respect to the ground. Approximately how high is it above the ground?
-3 m -4 m >2 m -1 m -none of these
A diver who weighs 500 N steps off a diving board that is 10 m above the water. The diver hits the water with kinetic energy of
-510 J. -500 J. >5000 J. -more than 5000 J. -10 J.
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?
-The energy is thermal energy before it hits the ground; it is kinetic energy after. -The energy is kinetic energy before it hits the ground; it is potential energy after. >The energy is kinetic energy before it hits the ground; it is thermal energy after. -The energy is potential energy before it hits the ground; it is thermal energy after.
If a ping pong ball and a golf ball are both moving in the same direction with the same amount of kinetic energy, the speed of the ping pong ball must be
-less than the golf ball. -the same as the golf ball. >more than the golf ball. -impossible to predict without additional information
An object at rest may also have
-momentum. -velocity. >potential energy. -kinetic energy. -speed.
If an object is raised twice as high, its potential energy will be
>twice as much. -four times as much. -half as much -impossible to determine unless the time is given.
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
-more than 100 J. -less than 100 J. >100 J. -need more information
A ball is projected into the air with 100 J of kinetic energy which is transformed to gravitational potential energy at the top of its trajectory. When it returns to its original level after encountering air resistance, its kinetic energy is
-more than 100 J. >less than 100 J. -100 J. -not enough information given
What is the unit of work?
-newton >joule -kg m/s -watt • Unit is the joule (J) or newton-meter (N*m)
A ball rolling down an incline has its minimum speed
>near the top of the incline. -half way down the incline. -at the end the incline. -impossible to predict without knowing the ball's mass -impossible to predict without knowing the size of the ball
Strictly speaking, more fuel is consumed by your car if an air conditioner, headlights, or even a radio is turned on. This statement is
-true only if the car's engine is running slowly. >true. -true only if the car's engine is running fast. -totally false.
When you weigh yourself on a bathroom scale on a slight incline instead of a level surface, your weight reading on the scale will be
-no different. -more. >less.
A ball rolling down an incline has its maximum kinetic energy at
-the top. -halfway down. -three-quarters of the way down. >the bottom.
If you push for a half hour or a whole hour against a stationary wall
-twice as much work is done during the half hour. -half as much work is done during the half hour. >no work on the wall is done in either case. -it is impossible to determine how much work is done.
Two planets in space gravitationally attract each other. If both the masses and distances are doubled, the force between them is
-twice as much. -four times as much. -half as much. -one-quarter. >none of the above
One's weightlessness in space has most to do with _______.
-one's mass >no support force no gravity -rotational effects
If Earth's mass decreased to one-half its original mass with no change in radius, then your weight would
-stay the same. -decrease to one-quarter. >decrease to half. -none of the above
When an automobile is braked to a stop, its kinetic energy is transformed to
-stopping energy. >heat. -energy of rest. -energy of motion. -potential energy.
Which produces a greater tidal effect in your body, the Moon or a 1-kg melon held at arm's length above your head?
-the Moon -both about equally >the melon
The work that is done when twice the load is lifted twice the distance is _______.
-the same >four times as much -twice as much -three times as much
Energy cannot be _______.
-transformed -transferred, transformed, or destroyed -transferred >destroyed
When the distance between two stars decreases by one-third, the force between them
>increases to nine times as much. -decreases by one-third. -decreases by one-half. -increases to twice as much. -none of the above
Principle of Conservation of Energy
E1=E2
Calculate the number of joules of kinetic energy a 1.4-kg book has when tossed at a speed of 2.8 m/s . Express your answer to two significant figures and include the appropriate units. *Kinetic energy = 12 mass × speed2 : KE = 12mv2
KE = 5.5 J
Consider a ball thrown straight up in the air. At what position is its kinetic energy at a maximum? Where is its gravitational potential energy at a maximum?
Kinetic energy is a maximum as soon as the ball leaves the hand. Potential energy is a maximum when the ball has reached its highest point.
At what point in its motion is the KE of a pendulum bob at a maximum? At what point is its PE at a maximum? When its KE is at half its maximum value, how much PE does it have relative to its PE at the center of the swing?
The KE of a pendulum is maximum at the bottom of its swing where its PE is minimum (or where we often take its PE to be zero). The PE of a pendulum is maximum at the top of its swing where it momentarily stops and its KE is zero. The total energy remains constant, E = KE + PE So when the pendulum's KE is half its maximum value, its PE is half its maximum value if we have counted its PE as zero at the bottom of its swing.
In what sense does the Moon "fall"?
The moon falls away from the straight line it would follow if there were no forces acting on it. It falls in a sense that if there were no gravity it would fall in a straight line. Due to the gravitational pull it is subjected to continuously circle the Earth.
Two cars are raised to the same elevation on service-station lifts. If one car is twice as massive as the other, how do their gains of potential energies compare?
The twice-as-massive car has twice the PE
Which has greater kinetic energy, a car traveling at 30 km/hr or a car of half the mass traveling at 60 km/hr?
>the 60 km/hr car -the 30 km/hr car -Both have the same kinetic energy. -More information is needed about the distance traveled.
Your weight is the force
>you exert against a supporting surface. -due to gravity only. -equal to your normal force on any surface.
Understanding Mass and Weight - Copy Learning Goal: To understand the distinction between mass and weight. The concepts of mass and weight are often confused. In fact, in everyday conversations, the word "weight" often replaces "mass," as in "My weight is seventy-five kilograms" or "I need to lose some weight." Of course, mass and weight are related; however, they are also different. Mass, as you recall, is a measure of the amount of matter an object has. This matter is able to resist acceleration. Newton's 2nd law demonstrates the relationship among an object's mass, its acceleration, and the net force acting on it: Fnet=ma. Mass is an intrinsic property of an object and is independent of the object's location. Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: W=mg, where W is the weight of an object, m is the mass of that object, and g is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the mass of the object and its "gravitational location". Part A Which of the following quantities represent mass? (Check all that apply.) Part B Which of the following quantities would be acceptable representations of weight? (Check all that apply.) Part C The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth, which properties of the rock change? Part D An object is lifted from the surface of a planet to an altitude equal to the radius of the planet (such that its distance from the center of the Earth is now doubled). As a result, which of the following changes in the properties of the object take place?
Part A -12.0 lbs >0.34 g >120 kg -1600 kN -0.34 m -411 cm -388 N Part B >12.0 lbs -0.34 g -120 kg >1600 kN -0.34 m -411 cm >388 N *Weight is a force and is measured in newtons (or kilonewtons, etc.) or in pounds (or tons, megatons, etc.) ~Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression W=GmM/r2, where W is the weight of the object, G is the gravitational constant, m is the mass of that object, M is mass of the planet, and r is the distance from the center of the planet to the object. If the object is on the surface of the planet, r is simply the radius of the planet.~ Part C -mass only >weight only -both mass and weight -neither mass nor weight Part D -mass increases; weight decreases -mass decreases; weight decreases -mass increases; weight increases -mass increases; weight remains the same >mass remains the same; weight decreases -mass remains the same; weight increases -mass remains the same; weight remains the same
Video: Apparent Weightlessness - Copy Part A How does the gravity in the Space Shuttle compare with the gravity on Earth's surface? Part B Why does the gravity at the Space Shuttle compare with the gravity on Earth the way it does? Part C Why do the astronauts in the Space Shuttle float around?
Part A -The gravity in the Space Shuttle is much smaller than the gravity on Earth's surface. >The gravity in the Space Shuttle is approximately equal to the gravity on the surface of the Earth. -The gravity in the Space Shuttle is much larger than the gravity on Earth's surface. Part B -In orbit, the Space Shuttle is not very close to the Earth. >In orbit, the Space Shuttle is about the same distance from the center of the Earth as it was when it was on the surface of the Earth. -In orbit, the Space Shuttle is much closer to the center of the Earth than it was when it was on the surface of the Earth. Part C -There is no gravity in the Space Shuttle because it is completely enclosed and shielded from the effects of gravity due to the Earth. -There is no gravity in the Space Shuttle because it is too far away from the center of the Earth. >The Space Shuttle is in free fall, so the shuttle and the astronauts inside it are continuously falling toward the Earth. They thus experience apparent weightlessness.
Video: Bowling Ball and Conservation of Energy Part A What happens the first time Dr. Hewitt lifts the bowling ball near his teeth and lets go? Part 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? Part C What happens the second time Dr. Hewitt lifts the bowling ball near his teeth and gives it a push? Part D Why does the bowling ball behave as it does when Dr. Hewitt lifts it and gives it a push?
Part A -The ball leaves Dr. Hewitt and returns to him, stopping short of the point where it was released. >The ball returns to Dr. Hewitt, stopping almost exactly at the point where it was released. -The ball leaves Dr. Hewitt and returns to him, going past the point where it was released. Part B -All of the initial energy of the ball was lost when the ball was released. >All of the initial energy of the ball was converted completely back to potential energy when the ball returned. -Some of the initial energy of the ball was lost, and it had less energy than it had at the beginning. Part C >The ball leaves Dr. Hewitt and returns to him, going past the point where it was released. -The ball leaves Dr. Hewitt and returns to him, stopping short of the point where it was released. -The ball returns to Dr. Hewitt, stopping almost exactly at the point where it was released. Part D -The ball's initial energy is lost. -The ball gains potential energy after it is released. >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.