Physics chapter 7
a) How much work is done when you push a create horizontally with 100 N across a 10 m factory floor? b) if the force of friction on the crate is a steady 70 N, show that the KE gained by the crate is 300 J. c) show that 700 J is turned into heat.
(a) You do F d = 100 N 10 m = 1000 J of work. (b) Because of friction, net work on the crate is less. KE = net work = net force distance = (100 N - 70 N)(10 m) = 300 J (c) So the rest, 700 J, goes into heating the crate and floor.
How much work is needed to lift a bag of groceries that weighs 200N to a height of 3m? How much work is needed to lift it twice as high?
-W= F x d W= 200 N x 3m W= 600 J - lifting the bag twice as high requires twice the work
A rifle of mass 2 kg is suspended by strings. The rifle fires a bullet of mass 0.01 kg at a speed of 200 m/s. What is the recoil velocity of the rifle?
1 m/s
Consider massive gliders that slide friction-free along a horizontal air track. Glider A has a mass of 1 kg, a speed of 1 m/s, and collides with Glider B that has a mass of 5 kg and is at rest. If they stick upon collision, find their speed after collision.
1/6 m/s
A 1000-kg car moving at 10 m/s brakes to a stop in 5 s. Find the average braking force.
2000N
In an ideal pulley system, a woman lifts an 80-N crate by pulling a rope downward with a force of 20 N. For every 1-meter length of rope she pulls downward, the crate rises by how much?
25 cm
A model airplane moves twice as fast as another identical model airplane. Compared with the kinetic energy of the slower airplane, what is the kinetic energy of the faster airplane ?
4 times as much
A shiny sports car at the top of a vertical cliff has a potential energy of 100 MJ relative to the ground below. Unfortunately, a mishap occurs and it falls over the edge. When it is halfway to the ground, find its kinetic energy?
50 MJ
Why does one get tired when pushing against a stationary wall when no work is done on the wall?
Although no work is done on the wall, work is nevertheless done on internal parts of your body (which generate heat).
What famous equation describes the relationship between mass and energy?
Einstein's E = mc^2
What does the work-energy theorem say about the speed of a satellite in circular orbit?
In accord with the theorem, once moving, no work is done on the satellite (because the gravitational force has no component parallel to motion), so no change in energy occurs. Hence the satellite cruises at a constant speed.
To combat wasteful habits, we often speak of "conserving energy," by which we mean turning off lights and hot water when they are not being used and keeping thermostats at a moderate level. In this chapter we also speak of "energy conservation." Distinguish between these two usages.
In the popular sense, conserving energy means not wasting energy. In the physics sense energy conservation refers to a law of nature that underlies natural processes. Although energy can be wasted (which really means transforming it from a more useful to a less useful form), it cannot be destroyed. Nor can it be created. Energy is transferred or transformed, without gain or loss. That's what a physicist means in saying energy is conserved.
When you are driving at 90 km/h, how much more distance do you need to stop compared with driving at 30 km/h?
Nine times farther. The car has nine times as much kinetic energy when it travels 3 times as fast. The friction force will ordinarily be the same in either case; therefore 9 times as much work requires 9 times as much distance.
Can an object have work?
No, unlike momentum or energy, work is not something that an object has. Work is something that an object does to some other object.
Why does the force of gravity do work on a car that rolls down a hill but no work when it rolls along a level part of the road
On the hill there is a component of gravitational force in the direction of the car's motion. This component of force does work on the car. But on the level, there is no component of gravitational force along the direction of the car's motion, so the force of gravity does no work in this case.
Belly-flop bernie dives from atop a tall flagpole into a swimming pool below. His potential energy at the top is 10,000 J. What is his kinetic energy when his kinetic energy when his potential energy reduces to 1000 J?
PE + KE = Total E; KE = 10,000 J - 1000 J = 9000 J.
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.
At what point in its motion is the KE of a pendulum bob at 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 bob is maximum where it moves fastest, at the lowest point; PE is maximum at the uppermost points. When the pendulum bob swings by the point that marks half its maximum height, it has half its maximum KE, and its PE is halfway between its minimum and maximum values. If we define PE = 0 at the bottom of the swing, the place where KE is half its maximum value is also the place where PE is half its maximum value, and KE = PE at this point. (By energy conservation: Total energy = KE + PE.)
Does an automobile consume more fuel when its air conditioner is turned on? When its lights are on? When its radio is on while it is sitting in the parking lot?
The answer to all these questions is yes. For energy consumed ultimately comes from the fuel. Even the energy taken from the battery must be given back to the battery by the alternator, which is turned by the engine, which runs from the energy of the fuel.
If a forklift is replaced with a new forklift that has twice the power, how much more dirt can it lift in the same amount of time? If it lifts the same dirt, how much faster can it operate?
The forklift that delivers twice the power will lift twice the load of dirt in the same time or the same load in half the time. Either way, the owner of the forklift is happy.
How much work is done in pushing the 100 N block of ice up the 4m long ramp?
W= f x d W= 50N x 4m W= 200 J
How much work is done in lifting the 100 N block of ice a vertical distance of 2 m?
W=f x d W= 100 N x 2m W= 200 J
When a rifle with a longer barrel is fired, the force of expanding gases effect does this have on the velocity of the emerging bullet?
When a rifle with a long barrel is fired, more work is done as the bullet is pushed through the longer distance. A greater KE is the result of the greater work, so of course, the bullet emerges with a greater velocity. (Note that the force acting on the bullet is not constant, but decreases with increasing distance inside the barrel.)
When the velocity of an object is doubled, by what factor is its momentum changed? By what factor is its kinetic energy changed?
When the velocity is doubled, the momentum is doubled and the KE is increased by a factor of 4. Momentum is proportional to speed, KE to speed squared.
Rows of wind powered generators are used in various windy locations to generate electric power. Does the power that is generated affect the speed of wind? That is, would locations behind the wind generators be windier if the generators weren't there?
Wind-powered generators take KE from the wind, so the wind is slowed by interaction with the blades. So, yes, it would be windier behind the wind generators if they weren't there.
Two people who weigh the same climb a flight of stairs. The person climbs the stairs in 30 s, and the second person climbs them in 40 s. Which person does more work? Which uses more power?
Work done by each is the same, for they reach the same height. The one who climbs in 30 s uses more power because work is done in a shorter time.
Does the international space station have gravitational PE? KE?
Yes to both, relative to Earth, because work was done to lift it in Earth's gravitational field and to impart speed to it.
Can an object have energy?
Yes, but in a relative sense. For example an elevated object may possess PE relative to the ground below, but none relative to a point at the same elevation. Similarly, the KE that an object has is relative to a frame of reference, usually earth's surface.
If your friend pushes a lawnmower 4 times as far as you do while exerting only half the force, which one of you does more work? How much more?
Your friend does twice as much work
Consider an imaginary miracle car that has 100 % efficient engine and burns fuel that has an energy content of 40 MJ per liter. If the air drag and overall frictional forces on the car traveling at highway speed is 500 N, how far could the car travel per liter of fuel at this speed?
distance = work / force distance = 40,000,000 J/L / 500 N distance = 80,000 m/L distance = 80 km/ L
