Physics: Energy
If the mass in a horizontal mass-spring system was doubled, the elastic potential energy in the system would change by a factor of
0 (no change).
An ideal spring has a spring constant (force constant) of 60 N/m. How much energy does it store when it is stretched by 1.0 cm?
0.0030 J
A 1.0-kg object moving in a certain direction has a kinetic energy of 2.0 J. It hits a wall and comes back with half its original speed. What is the kinetic energy of this object at this point?
0.50 J
A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal ideal spring with spring constant (force constant) of 2.0 ¥ 10 6N/m. What is the maximum distance the spring compresses?
0.68 m
The amount of mechanical kinetic energy possessed by a 0.25-kilogram ball rolling at a speed of 2.5 meters per second is ____ joules.
0.78
Lifting a 70-kilogram barbell 2.0 meters above the floor increases its potential energy by about:
1,400 joules.
What is the minimum energy needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s?
1.10 MJ
Jonah is pushing his younger sister, Jessica, on a swing. If Jessica weighs 35 kilograms, how much higher above the ground must Jonah push her to increase her potential energy by 525 joules?
1.5 meters
An object hits a wall and bounces back with half of its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy of the object?
1/4
How high a hill would a 75-kg hiker have to climb to increase her gravitational potential energy by 10,000 J?
14m
A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s. How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible.
15 m/s
An ideal spring stretches by 21.0 cm when a 135-N object is hung from it. If instead you hang a fish from this spring, what is the weight of a fish that would stretch the spring by 31.0 cm
199 N
Assuming negligible friction, what spring constant (force constant) would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?
20 N/cm
The figure shows a famous roller coaster ride. You can ignore friction. If the roller coaster leaves point Q from rest, what is its speed at the top of the 25-m peak (point S)?
22 m/s
Ball A has triple the mass and speed of ball B. What is the ratio of the kinetic energy of ball A to ball B.
27
How much kinetic energy does a 0.30-kg stone have if it is thrown at 44m/s
290 J
When you drop a pebble from height H, it reaches the ground with kinetic energy K if there is no air resistance. From what height should you drop it so it will reach the ground with twice as much kinetic energy?
2H
What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance.)
34 MJ
A bead is moving with a speed of 20 m/s at position A on the track shown in the figure. This track is friction-free, and there is no appreciable air resistance. What is the speed of the bead at point C?
34 m/s
If the displacement of a horizontal mass-spring system was doubled, the elastic potential energy in the system would change by a factor of
4
In the figure, a ball hangs by a very light string. What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A, which is 1.0 m above the bottom of the swing?
4.4 m/s
A prankster drops a water balloon from the top of a building. If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground, how tall is the building? Neglect air resistance.
45 m
A 10-kg mass, hung by an ideal spring, causes the spring to stretch 2.0 cm. What is the spring constant (force constant) for this spring?
49 N/cm
When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed?
4H
A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect all friction and assume the spring is ideal)?
6.0 m
A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls. At what speed will its gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy?
6.3 m/s
How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?
7.1 m/s
Shawna, who weighs 54 kilograms, is roller blading on a level surface. If she is rolling at 12 meters per second, to what height would she roll up an incline before stopping? (Assume there is no friction.)
7.3 meters
For which of the following situations is the conservation of mechanical energy most likely to be a valid assumption?
A soccer ball flies through the air.
A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct? (There could be more than one correct choice.)
As they reach the ground, the 1-kg ball will be moving faster than the 2-kg ball. Both balls will reach the ground with the same kinetic energy.
Two identical grasshoppers jump into the air with the same initial speed and experience no air resistance. Grasshopper A goes straight up, but grasshopper B goes up at a 66° angle above the horizontal. Which of the following statements about these grasshoppers are correct? (There could be more than one correct choice.)
At their highest point, both of them have the same amount of mechanical energy. At their highest point, grasshopper B is moving faster than grasshopper A. At their highest point, grasshopper A has more gravitational potential energy than grasshopper B
The diagram below represents a cart traveling from left to right along a friction-less surface with an initial speed of 3 m/sec. At what point is the potential energy least?
B
You and your friend, who weighs the same as you, want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top.
Both of you have the same amount of gravitational potential energy at the top.
Two frisky otters slide down frictionless hillsides of the same height but different slopes. The slope of the hill of otter 1 is 30°, while the slope of the hill of otter 2 is 60°. If both start from rest, which otter is moving faster when she reaches the bottom of her hill?
Both otters have the same speed at the bottom.
A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There could be more than one correct choice.)
Both rocks have the same speed when they reach the ground. When they reach the ground, the heavier rock has more kinetic energy than the lighter rock.
What is the potential energy of a 1.0 kg mass 1.0 m above the ground?
Given: m=1.0kg h=1.0m g=9.81m/s 2 Solution: PE=mgh= (1.0kg)(9.81m/s)^2 =9.8J
A 3.00 kg toy falls from a height of 1.00 m. What will the kinetic energy of the toy be just before the toy hits the ground? (Assume no air resistance and that g = 9.81 m/s)^2
Given: m=3.00kg h=1.00m g=9.81m/s^2 Solution: KE=mv^2 PE=mgh =(3.00kg)(9.81m/s)^2(1.00m) =29.4J
What is the magnitude of the centripetal force on the bicycle?
Given: m=43kg vt =2.0m/s r=2.0m Solution: Fc=mvt^2/r = (43kg)(2.0m/s)^2/2.0m =86N
A child rides a bicycle in a circular path with a radius of 2.0 m. The tangential speed of the bicycle is 2.0 m/s. The combined mass of the bicycle and the child is 43 kg. ____ 55. What is the magnitude of the bicycle's centripetal acceleration?
Given: vt =2.0m/s r=2.0m Solution: ac = vt^2/r = (2.0m/s)^2/2.0m =2.0m/s^2
How much elastic potential energy is stored in a bungee cord with a spring constant of 10.0 N/m when the cord is stretched 2.00 m?
Given: k=10.0N/m x=2.00m Solution: PE= 1/2 kx^2 = 1/2 (10.0N/m)(2.00m)^2 =20.0 J
What is the kinetic energy of a 0.135 kg baseball thrown at 40.0 m/s?
Given: m=0.135kg v=40.0m/s Solution: KE= 1/2 mv 2 = 1/2 (0.135kg)(40.0m/s) 2 =108 J
A 20-kilogram object falls 2.0 meters to the floor. At what point in its fall does the kinetic energy of a body equal its potential energy?
Halfway to the floor
A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which of the following statements about these frogs are correct? (There could be more than one correct choice.)
Just as they leave the ground, the lighter frog is moving faster than the heavier frog. Both frogs reach the same maximum height.
Which of the following formulas would be used to directly calculate the kinetic energy of an object with mass m bouncing up and down on a spring with spring constant k?
KE= 1/2 mv^2
A truck has four times the mass of a car and is moving with twice the speed of the car. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say that
Kt = 16Kc
What are the units for a spring constant?
N/m
Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s?
The 500-kg object
A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct? (There could be more than one correct choice.)
The darts both have the same kinetic energy just as they move free of the spring. The lighter dart leaves the spring moving faster than the heavy dart. Both darts had the same initial elastic potential energy.
A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small. Which of the following statements about these stones are correct? (There could be more than one correct choice.)
The initial height of the light stone is greater than the initial height of the heavy stone. Just as it reaches the ground, the light stone is traveling faster than the heavy stone. The stones both have the same kinetic energy just as they reach the ground.
A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the following statements about these darts are correct? (There could be more than one correct choice.) a. The heavy dart goes higher than the light dart.
The light dart goes higher than the heavy dart. At the maximum height, both darts have the same gravitational potential energy.
A stone can slide down one of four different frictionless ramps, as shown in the figure. For which ramp will the speed of the ball be the greatest at the bottom?
The speed of the ball will be the same for all ramps.
A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance?
The speed will be the same in all cases.
A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. If the ground at the base of the cliff is level, which rock hits the ground with the greatest speed if there is no air resistance?
They all hit the ground with the same speed.
A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill with no air resistance. Which object rises to a greater height?
They both slide to exactly the same height.
Which of the following is a true statement about the conservation of energy?
Total energy is always conserved.
Gravitational potential energy is always measured in relation to
a zero level.
The equation for determining gravitational potential energy is PE g= mgh. Which factor(s) in this equation is (are) not intrinsic to an object?
both g and h
What is the term for the net force directed toward the center of an object's circular path?
centripetal force
Which of the following energy forms is not involved in hitting a tennis ball?
chemical potential energy
Which form of energy is involved in weighing fruit on a spring scale?
elastic potential energy
A stone is held at a height h above the ground. A second stone with four times the mass of the first one is held at the same height. The gravitational potential energy of the second stone compared to that of the first stone is
four times as much
Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be
four times that of Bill's ball.
What kind of force provides the centripetal force on the bicycle?
friction
Which of the following can be a centripetal force?
friction, gravity, tension
An object falls without friction near Earth's surface. The loss of its potential energy is equal to its:
gain in kinetic energy.
Which of the following is a form of mechanical energy?
gravitational potential energy
The centripetal force on an object in circular motion is
in the plane of the object's motion and perpendicular to the tangential speed.
The centripetal force on an object in circular motion is
in the same direction as the centripetal acceleration.
As the speed of a moving object doubles, the amount of mechanical kinetic energy that it possesses:
increases by four times.
A ball is whirled on a string, then the string breaks. What causes the ball to move off in a straight line?
inertia
When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?
inertia
When an object is moving with uniform circular motion, the object's tangential speed
is constant.
When an object is moving with uniform circular motion, the centripetal acceleration of the object
is directed toward the center of motion.
Which of the following energy forms is associated with an object in motion?
kinetic energy
The main difference between kinetic energy and potential energy is that
kinetic energy involves motion, and potential energy involves position.
Which of the following refers to the sum of kinetic energy and all forms of potential energy?
mechanical energy
Which of the following are examples of consersable quantities?
mechanical energy and mass
Horses that move with the fastest linear speed on a merry-go-round are located
on the outside
Energy that is stored due to the position of an object may be called ____ energy.
potential
Which of the following energy forms is associated with an object due to its position?
potential energy
Which of the following parameters does not depend on how resistant a spring is to being compressed or stretched?
relaxed length
Potential energy increases as a marble:
slows rolling up an incline.
When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high?
square root of 2v
What term describes a change in the speed of an object in circular motion?
tangential acceleration
Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground
the heavier one will have twice the kinetic energy of the lighter one.
Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2?
v1 = v2
When swinging a yoyo in a horizontal loop, when would the tension force be the greatest?
when you have a short string going fast
