Physics chapter 6 (work, energy, power)

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For each situation, tell whether the net work done on a soccer ball is (a) positive, (b) negative, or (c) 0. (1) You carry the ball out to the field, walking at constant speed. (2) You kick the stationary ball, starting it flying through the air. (3) The ball rolls along the field, gradually coming to a halt.

(1) (c): Kinetic energy doesn't change, so the net work done on the ball is zero. (2) (a): Kinetic energy increases, so the net work is positive. (3) (b): Kinetic energy decreases, so the net work is negative.

Two objects are each displaced the same distance, one by a force FF pushing in the direction of motion and the other by a force 2F pushing at 45° to the direction of motion. Which force does more work? (a)F; (b)2F; (c) they do equal work

(b) 2F does √2 more work than F does. That's because 2F's component along the direction of motion is 2F cos 45°,2F cos 45°, or 2F√2 /2 =F√2.

Three forces have magnitudes in newtons that are numerically equal to these quantities: (a)x, (b)x2, and (c)√x, where x is the position in meters. Each force acts on an object as it moves from x=0 to x=1m. Notice that all three forces have the same values at the two endpoints—namely, 0 N and 1 N. Which of the forces (a), (b), or (c) does the most work? Which does the least?

(c) √x does the most work. (b) x2 does the least. You can see this by plotting these two functions from x=0 to x=1 and comparing the areas under each. The case of x is intermediate.

Albert Einstein lowers a book of mass m downward a distance h at constant speed v. The work done by the force of gravity _____, the force of albert's hand ________, the net force on the book is _______

+,-,0

An atomic bomb explodes. Is energy conserved in the nuclear reactions of the bomb? Is matter (i.e. mass) conserved?

-Yes. Energy is always conserved. -No, mass is not conserved. Mass is a form of energy and can be converted into other forms of energy. In a chemical reaction, the total mass of the products is less than the mass of the reactants by about 1 part in a billion - too small to measure, but there is a mass loss.

A projectile is fired upward through air with an initial speed v0. A short time later, it comes back down and has a final speed v < v0 . Air resistance is NOT negligible. What was the sign of the work done by friction during the flight? The work done by friction WFRIC during the flight is

-negative. The direction of the force of friction is always opposite the direction of motion, both on the way up and on the way down. So the work done is negative. - delta KE

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. (Assume no air resistance.) Just before hitting the ground, the heavier marble has..

..twice as much kinetic energy as the lighter one. (They both have the same speed on impact).

If spring is relaxed then x=

0

A box sits on a horizontal table. A string with tension T pulls to the right, but static friction between the box and the table prevents the box from moving. 1) What is the magnitude of the static frictional force acting on the box?

0, since the ball is the accelerating the static friction will be zero

How to compute the work done if fnet does not equal 0 and object moves along a curvy path?

1. Break the path up into large number of very small straight line segment 2. if segment delta(r) is very small, then force is constant for that segment 3. Then the work ΔW done in moving the width Δx of one such rectangle is approximately F(x) Δx, where F(x) is the force at the midpoint x of that rectangle. 4. W=limΔx→0 ∑F(xi) Δx (where xi is the midpoint)

A scalar product is _________ and ____________.

1. commutative: A⋅B=B⋅A 2. distributive: A⋅(B+C)=A⋅B+A⋅C

kinetic energy formula

1/2 mass x speed^2

Elastic Energy

1/2kx2

One horsepower is equal to

746 watts

A orange and cantalope is dropped from a certain distance. Which has more kinetic energy when it is dropped?

Although both has similar speed, The cantalope will have more kinetic energy because it has more mass.

Scalar product of two vectors

A⋅B=AB cos θ

The scalar product can also be written in component:

A⋅B=AxBx +AyBy +AzBz

Spring Force

F = -kx where k is the spring constant and the minus sign shows that the spring force is opposite the direction of the displacement.

Is force and work the same?

Force and work are directly proportional to each other, while force and displacement are indirectly propotional. The equation showing the relationship is W= Fd. W represents work measured in joules; F represents force in newtons; and d represents distance in meters

An elastic cord used in bungee jumping is normally x length long and has a k constant. At the lowest point in a jump, the cord length has doubled. Is the work done as the cord stretches its final meter greater than, less than, or equal to the work done in the first meter of stretch?

Greater than the word done in the first meter because at first the cord exerts very little force.

How does velocity impact the stopping distance?

If v is doubled, then the car skids 4 times as far.

The purpose of definite integral in computing work done when the velocity is not constant

It tells us to divide the interval from x1 to x2 into many small rectangles of width Δx, to multiply the value of the function F(x) at each rectangle by the width Δx, and to sum those products. In the limit of infinitely many infinitesimally small rectangles, the result of this process gives us the value of the definite integral.

kinetic energy

Like velocity, kinetic energy is a relative term; its value depends on the reference frame in which it's measured. But unlike velocity, kinetic energy is a scalar. And since it depends on the square of the velocity, kinetic energy is never negative.

Gravity is a conservative force. Is the force of friction a conservative force? A) Yes B) No

No. The work done by the force of friction is path-dependent

Instantaneous power

P = dW / dt average power taken in a limit at an arbitrarily small time interval.

Equation deriving of velocity, power and applied force

P=F⋅v

Power formula

P=W/t

What would be the total work done by gravity along a zig zag track up the rocky mountains?

Since the weight force is always perpendicular to the horizontal segment, therefore, the total work done by gravity along this path is just the sum of work done by gravity along the vertical segments.

A newspaper reports that a new power plant will produce "50 megawatts per hour." What's wrong with this statement?

The megawatt is a unit of power; the "per time" is already built in. A correct statement would be that the power plant will produce "energy at the rate of 50 megawatts."

If instead of moving part way around a square, the mass where taken on a long and tortuous journey to the Moon, Tibet, and Lithuania and then returned to the same finish point as before, would the total work done by gravity be the ..

The same. The total work done by gravity is independent of the path taken between the start and finish.

An apple is initially sitting on the bottom shelf of a pantry. A hungry physics student picks up the apple to eat it, but changes her mind and puts the apple down on a shelf somewhere above its original location. During this process, the total work done on the apple by all forces is:

The total work done on the apple by all the forces is equal to the change in kinetic energy of the apple. SInce the apple starts out at rest and ends up at rest, the change in its kinetic energy is zero. This means that the total work done on it must also be zero.

Amount of work done in terms of power.

W=P Δt

The airline passenger exerts a 60-N force on her luggage, pulling at 35° to the horizontal. How much work does she do in pulling the luggage 45 m on a level floor?

W=fd so, 60(cos35) times 45=2.2KJ

The person pushes with a force of 650 N, moving the car a distance of 4.3 m. How much work does he do?

W=fd so, 650 times 4.3 = 2.8KJ

Work done against gravity

When an object moves upward or downward on an arbitrary path, the angle between its displacement and the gravitational force varies. But we don't need integrals. so, W=mgh

A box is initially sliding across a frictionless floor toward a spring that is attached to a wall on the right. The box hits the end of the spring and compresses it, eventually coming to rest for an instant before bouncing back the way it came. The work done by the spring on the box as the spring compresses is:

While the spring is compressing, the force it exerts on the box is in the opposite direction to the displacement of the box, hence the work it does on the box is negative.

Difference between energy and power

Work is defined as the process of energy transfer to the motion of an object through the application of force. Power is defined as the amount of energy transferred in unit time.

A rock of mass m is twirled on a string in a horizontal plane. The work done by the tension in the string on the rock is..

Wtension = 0 , since in any small(infinitesimal) time interval, the tension force is perpendicular to the displacement.

A car moves of mass m moving with speed v suddenly applies the brakes and slows to a stop. Suppose I ask "What was the work done on the car by the force of friction?" Do you have enough information to answer the question?

Yes. In this case, the net force is the force of friction , since the other forces (normal force and gravity) cancel. Work-KE Theorem says Wnet = delta KE. So Wnet = Wfric = KEf - KEi = - (1/2)mv2 .

How does work change when you make the system heavier?

You do more work, as you are applying more force on the system

Explain carrying a box through work.

You have to apply an upward force on the box as you climb the stairs. Define the box as your system, and the force you apply is an external force that does work on the system. Thus you transfer energy from your body to the box by doing mechanical work.

A projectile is fired upward with an initial speed v on an airless world. A short time later, it comes back down and has a final speed v (just before it hits the ground). What was the sign of the total work done by the force of gravity during the flight?

Zero. Two ways to see this: Method I. The negative work done by gravity on the way up is -mgh, and this is cancelled by the positive work done by gravity +mgh, on the way down. Method II. By the Work-KE Theorem, Wnet = delta KE = 0. Here the net force is the force of gravity, so Wgrav = 0.

conservation of energy

a principle stating that energy cannot be created or destroyed, but can be altered from one form to another.

A block slides on a table pulled by a string attached to a hanging weight. In case 1 the block slides without friction and in case 2 there is kinetic friction between the sliding block and the table. 1) In which case is the tension in the string the biggest?

case 2 It not only has the pull, but it has a pull back from static friction making it resist movement and increasing tension

Energy and Systems

energy flows both within a system and across its boundaries, as well as transformations between different types of energy within the system.

Explain the situation using work and force: A woman pulls her luggage

he person pulling her luggage does work equal to only the horizontal component of the force she applies times the distance the luggage moves.

Recall that ˆ i and ˆ j are the unit vectors in the +x and +y directions. What is the value of ˆ i j and what is i i ?

i j = 0 i i = 1

If spring is compressed then x=

negative

A force acting in the right angle of the motion does ________

no work

If a spring is stretched from its relaxed length then the x=

positive

A 1 kg mass is moved part way around a square loop as shown. The square is 1 meter on a side and the final position of the mass is 0.5 m below its original position. Assume that g = 10 m/s2 . What is the work done by the force of gravity during this journey?

positive 5 J

A box sits on the horizontal bed of a truck accelerating to the left as shown. Static friction between the box and the truck keeps the box from sliding around as the truck drives. 1) The work done on the box by the static frictional force as the accelerating truck moves a distance D to the left is?

positive because the static friction moves in the same direction as acceleration

One end of a spring is fixed in place. I stretch the spring by pulling on the other end. What is the sign of the work done by the force from my hand?

positive. No matter which way I pull, the force I exert is in the same direction as the displacement. When force and displacement are in the same direction, the work done is positive.

Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of of a string. 1) In which case does the object have the biggest total work done on it by all forces during its motion?

same

Work is a _____ quantity

scalar

Work-Kinetic Energy Theorem

the net work done by all the forces acting on an object is equal to the change in the object's kinetic energy

Explain the situation using work and force: A man pushes a car forward.

the person pushing the car does work equal to the force he applies times the distance the car moves.

Power definition

the rate at which work is done

Explain the situation: A waiter carries a tray pushing it upward

the waiter does no work on the tray as he carries it at constant velocity. Why not? Because the force on the tray is vertical while the tray's displacement is horizontal; there's no component of force in the direction of the tray's motion.

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding as the truck accelerates to the left as shown. 1) Which of the following diagrams best describes the static frictional force acting on the box?

to the left because static friction is towards the same way as acceleration

formula for work done by weight

w=-mgdelta y (this does not depend on the path taken but only on the difference of height initially to final

When power insn't constant _________

we can consider small amounts of work ΔW, each taken over so small a time interval Δt that the power is nearly constant. Adding all these amounts of work and taking the limit as Δt becomes arbitrarily small, we have W=limΔt→0 ∑P Δt=integral(t2 to t1)P dt where t1 and t2 are the beginning and end of the time interval over which we calculate the work.

a negative work is

when force acts in the opposite direction as the motion

A positive work is

when force acts in the same direction as the motion

A car drives up a hill with constant speed. 1) Which statement best describes the total work done on the car by all forces as it moves up the hill with a constant speed?

zero, because the net force is zero, work will also be zero


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