chapter 9 - energy

Question 1

what is kinetic energy ?

Answer 1

Kinetic energy is the energy of motion. All moving objects have kinetic energy. The more massive an object or the faster it moves, the larger its kinetic energy.

Question 2

what is potential energy ?

Answer 2

Potential energy is stored energy associated with an object’s position. The roller coaster’s gravitational potential energy depends on its height above the ground.

Question 3

what is thermal energy ?

Answer 3

Thermal energy is the sum of the microscopic kinetic and potential energies of all the atoms and bonds that make up the object. An object has more thermal energy when hot than when cold.

Question 4

the most important step in energy analysis is to identify the system
can you explain why ?

Answer 4

Why? Because energy is not some disembodied, ethereal substance; it’s the energy of something. Specifically, it’s the energy of a system.

designate as Esys

Question 5

what is a system ?

Answer 5

those objects whose motion and interactions we wish to analyze

Question 6

environement ?

Answer 6

objects external to the system but exerting forces on the system.

Question 7

can an system lose energy ?

what is the exception

Answer 7

Within the system, energy can be transformed without loss. Chemical energy can be transformed into kinetic energy, which is then transformed into thermal energy. As long as the system is not interacting with the environment, the total energy of the system is unchanged.

The energy of an isolated system—one that doesn’t interact with its environment—does not change. We say it is conserved.

Question 8

what the system interact with the environment , what happens to the system ?

Answer 8

But systems often do interact with their environment. Those interactions change the energy of the system, either increasing it (energy added) or decreasing it (energy removed). We say that interactions with the environment transfer energy into or out of the system.

Question 9

there are two ways to transfer energy

named them

Answer 9

Interestingly, there are only two ways to transfer energy. One is by mechanical means, using forces to push and pull on the system. A process that transfers energy to or from a system by mechanical means is called work, with the symbol W.

. The second is by thermal means when the environment is hotter or colder than the system. A process that transfers energy to or from a system by thermal means is called heat.

Question 10

gives some example of energy transfers

Answer 10

Putting a shot
System: The shot (ball)

Transfer: W→K

The athlete (the environment) does work pushing the shot to give it kinetic energy.

example 2:

Pulling a slingshot
System: The slingshot

Transfer: W→U

The boy (the environment) does work by stretching the rubber band to give it potential energy.

example 3:
A falling diver
System: The diver and the earth

Transformation: U→K

The diver is speeding up as gravitational potential energy is transformed into kinetic energy.`

Question 11

kinetic energy equation ?

and explain it a bit

Answer 11

K=1/2mv^2
Kinetic energy is energy of motion. It depends on the particle’s mass and speed but not on its position. Furthermore, kinetic energy is a property or characteristic of the system.

Question 12

units for kinetic energy

Answer 12

The unit of kinetic energy is mass multiplied by velocity squared. In SI units, this is kg m2/s2. Because energy is so important, the unit of energy is given its own name, the joule. We define

1 joule = 1 J = 1 kg m^2/s^2

Question 13

stop to think 9.1
A 1000 kg car has a speed of 20 m/s. A 2000 kg truck has a speed of 10 m/s. Which has more kinetic energy?

The car.

The truck.

Their kinetic energies are the same.

Answer 13

a)
Kinetic energy depends linearly on the mass but on the square of the velocity. A factor of 2 change in velocity is more significant than a factor of 2 change in mass.

Question 14

unit for work

Answer 14

joules

Question 15

A 5.0 kg cannonball is fired straight up at 35 m/s. What is its speed after rising 45 m?

Answer 15

18 m/s

Question 16

the signs of work

Answer 16

Work can be either positive or negative, but some care is needed to get the sign right when calculating work. The key is to remember that work is an energy transfer. If the force causes the particle to speed up, then the work done by that force is positive. Similarly, negative work means that the force is causing the object to slow and lose energy.

Question 17

how to det. the sign of work ?

Answer 17

The sign of W is not determined by the direction the force vector points. That’s only half the issue. The displacement Δs also has a sign, so you have to consider both the force direction and the displacement direction. As Figure 9.4 shows, work is positive when the force acts in the direction of the displacement (causing the particle to speed up). Similarly, work is negative when force and displacement are in opposite directions (causing the particle to slow). And there’s no work at all (W = 0) if the particle doesn’t move!

Question 18

Stop to Think 9.2

A rock falls to the bottom of a deep canyon. Is the work done on the rock by gravity positive, negative, or zero?

Answer 18

Positive. The force (gravity) and the displacement are in the same direction. The rock gains kinetic energy.

Question 19

Force perpendicular to the displacement:

Answer 19

a force perpendicular to the displacement does not change the particle’s speed; it is neither speeding up nor slowing down. Its energy is not changing, so no work is being done on it. A force perpendicular to the displacement does no work.

Question 20

multiple forces on a sys?

Answer 20

If multiple forces act on a system, their works add. That is, ΔK = Wtot, where the total work done is

(9.11)
Wtot=W1+W2+W3+⋯

Question 21

Multiparticle systems

Answer 21

If a system has more than one particle, the system’s energy is the total kinetic energy of all the particles:

(9.12)
Esys=Ktot=K1+K2+K3+⋯
Ktot is truly a system energy, not the energy of any one particle. How does Ktot change when work is done? You can see from its definition that ΔKtot is the sum of all the individual kinetic-energy changes, and each of those changes is the work done on that particular particle. Thus

You must find the work done on each particle, then sum those to find the total work done on the system.

Question 22

two key idea for work and system ?

Answer 22

a system has energy and (2) work is a mechanical process that changes the system’s energy.

Question 23

work, explain it

Answer 23

Specifically, it is a process that changes a system’s energy by mechanical means—pushing or pulling on it with forces. We say that work transfers energy between the environment and the system.

Question 24

if the work done is not parallel to the floor

which equation do we use ?

Answer 24

W=F(Δr)cosθ(work done by a constant force)

where θ is the angle between the force and the particle’s displacement Δr⃗ .

Question 25

if the work done is not parallel to the floor

which equation do we use ?

Answer 25

W=F(Δr)cosθ(work done by a constant force)

where θ is the angle between the force and the particle’s displacement Δr⃗ .

Question 26

Example 9.2 Pulling a suitcase
A strap inclined upward at a 45° angle pulls a suitcase 100 m through the airport. The tension in the strap is 20 N. How much work does the tension force do on the suitcase?

Answer 26

W=T(Δx)cosθ
=(20N)(100m)cos45∘
=1400J

Question 27

when is work positive ?

and talk about energy transfer

Answer 27

its positive at 0 degree 
or less than 90 degrees 
energy is transferred into the system 
the particles speeds up 
k increases

Question 28

when is work 0

Answer 28

at 90 degrees
no energy is transferred
speed and k are constant

Question 29

when is work negative

Answer 29

>90 degrees 
or point in opposite direction of displacement
energy is transferred out of the system 
the particle slows down
k decreases

Question 30

hint for sign of W

Answer 30

Think about whether the force is trying to increase the particle’s speed (W > 0) or decrease the particle’s speed (W < 0).

Question 31

Example 9.3 Launching a rocket
A 150,000 kg rocket is launched straight up. The rocket motor generates a thrust of 4.0 × 106 N. What is the rocket’s speed at a height of 500 m?

Answer 31

130 m/s

Question 32

Stop to Think 9.4
A crane uses a single cable to lower a steel girder into place. The girder moves with constant speed. The cable tension does work WT and gravity does work WG. Which statement is true?

WT is positive and WG is positive.

WT is positive and WG is negative.

WT is negative and WG is positive.

WT is negative and WG is negative.

WT and WG are both zero.

Answer 32

c. The upward tension force is opposite the displacement, so it does negative work. The downward gravitational force is parallel to the displacement, so it does positive work.

Question 33

a dot product must have….

Answer 33

a dot symbol between the two vector
A . B
The notation A⃗ B⃗ , without the dot, is not the same thing as A⃗ . B⃗ . The dot product is also called the scalar product because the value is a scalar.

Question 34

Example 9.4 Calculating a dot product

Compute the dot product of the two vectors in Figure 9.10.

Answer 34

A⃗ ⋅B⃗ =ABcosα
=(3)(4)cos30∘
=10.4

Question 35

Example 9.5 Calculating a dot product using components

Compute the dot product of A =3i +3j and B =4i −j .

Answer 35

A⋅B =AxBx+AyBy
=(3)(4)+(3)(−1)
=9

Question 36

equation for work

Answer 36

W=F⃗ ⋅Δr⃗ (work done by a constant force)

Question 37

Example 9.6 Calculating work using the dot product
A 70 kg skier is gliding at 2.0 m/s when he starts down a very slippery 50-m-long, 10° slope. What is his speed at the bottom?

Answer 37

13 m/s

While in the midst of the mathematics of calculating work, do not lose sight of what the energy principle is all about. It is a statement about energy transfer: Work causes a particle’s kinetic energy to either increase or decrease.

Question 38

Stop to Think 9.5
Which force does the most work as a particle undergoes displacement Δr⃗ ?

The 10 N force.

The 8 N force.

The 6 N force.

They all do the same amount of work.

Answer 38

c. W=F(Δr)cosθ. The 10 N force at 90° does no work at all. Because cos60∘=1/2, the 8 N force does less work than the 6 N force.

Question 39

zero-work situations

Answer 39

The most obvious is when the object doesn’t move (Δs=0). If you were to hold a 200 lb weight over your head, you might break out in a sweat and your arms would tire. You might feel that you had done a lot of work, but you would have done zero work in the physics sense because the weight was not displaced and thus you transferred no energy to it. A force acting on a particle does no work unless the particle is displaced.

Question 40

Last, consider the roller skater in Figure 9.15 who straightens her arms and pushes off from a wall. She applies a force to the wall and thus, by Newton’s third law, the wall applies a force F⃗ W on S to her. How much work does this force do?

Answer 40

Surprisingly, zero. The reason is subtle but worth discussing because it gives us insight into how energy is transferred and transformed. The skater differs from suitcases and rockets in two important ways. First, the skater, as she extends her arms, is a deformable object. We cannot use the particle model for a deformable object. Second, the skater has an internal source of energy. Because she’s a living object, she has an internal store of chemical energy that is available through metabolic processes.

Although the skater’s center of mass is displaced, the palms of her hands—where the force is exerted—are not. The particles on which force FW on S acts have no displacement, and we’ve just seen that there’s no work without displacement. The force acts, but the force doesn’t push any physical thing through a displacement. Hence no work is done.

Question 41

But the skater indisputably gains kinetic energy. How?

Answer 41

Recall, from the energy overview that started this chapter, that the full energy principle is ΔEsys = Wext. A system can gain kinetic energy without any work being done if it can transform some other energy into kinetic energy. In this case, the skater transforms chemical energy into kinetic energy. The same is true if you jump straight up from the ground. The ground applies an upward force to your feet, but that force does no work because the point of application—the soles of your feet—has no displacement while you’re jumping. Instead, your increased kinetic energy comes via a decrease in your body’s chemical energy. A brick cannot jump or push off from a wall because it cannot deform and has no usable source of internal energy.

Question 42

Example 9.7 Using work to find the speed of a car
A 1500 kg car is towed, starting from rest. Figure 9.16 shows the tension force in the tow rope as the car travels from x = 0 m to x = 200 m. What is the car’s speed after being pulled 200 m?

Answer 42

26 m/s

Question 43

Example 9.7 Using work to find the speed of a car
A 1500 kg car is towed, starting from rest. Figure 9.16 shows the tension force in the tow rope as the car travels from x = 0 m to x = 200 m. What is the car’s speed after being pulled 200 m?

Answer 43

26 m/s

Question 44

what is restoring force ?

Answer 44

A force that restores a system to an equilibrium position is called a restoring force.

Question 45

elastic ?

ex ?

Answer 45

Objects that exert restoring forces are called elastic.

The most basic examples of elasticity are things like springs and rubber bands, but other examples of elasticity and restoring forces abound. For example, the steel beams flex slightly as you drive your car over a bridge, but they are restored to equilibrium after your car passes by. Nearly everything that stretches, compresses, flexes, bends, or twists exhibits a restoring force and can be called elastic.

Question 46

hooke’s law ?

Answer 46

(FSp)s=−kΔs

The minus sign is the mathematical indication of a restoring force, and the constant k—the absolute value of the slope of the line—is called the spring constant of the spring. The units of the spring constant are N/m. This relationship between the force and displacement of a spring was discovered by Robert Hooke, a contemporary (and sometimes bitter rival) of Newton. Hooke’s law is not a true “law of nature,” in the sense that Newton’s laws are, but is actually just a model of a restoring force. It works well for small displacements from equilibrium, but Hooke’s law will fail for any real spring that is compressed or stretched too far.

Question 47

ideal spring.

Answer 47

A hypothetical massless spring for which Hooke’s law is true at all displacements

Question 48

the spring constant k

explained

Answer 48

The spring constant k is a property that characterizes a spring, just as mass m characterizes a particle. For a given spring, k is a constant—it does not change as the spring is stretched or compressed. If k is large, it takes a large pull to cause a significant stretch, and we call the spring a “stiff” spring. A spring with small k can be stretched with very little force, and we call it a “soft” spring.

Question 49

Example 9.8 Pull until it slips
Figure 9.18 shows a spring attached to a 2.0 kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 5.0 cm/s. The spring constant is 50 N/m, and the coefficient of static friction between the block and the surface is 0.60. The spring is at its equilibrium length at t = 0 s when the train starts to move. When does the block slip?

Answer 49

4.7 s

This example illustrates a class of motion called stick-slip motion. Once the block slips, it will shoot forward some distance, then stop and stick again. As the train continues, there will be a recurring sequence of stick, slip, stick, slip, stick….

Question 50

which equations we used for work done by spring ?

Answer 50

W=−(1/2k(Δsf)^2−1/2k(Δsi)^2)

the work done by a spring is energy transferred to the object by the force of the spring.

Question 51

Example 9.9 Using the energy principle for a spring

The “pincube machine” was an ill-fated predecessor of the pinball machine. A 100 g cube is launched by pulling a spring back 12 cm and releasing it. The spring’s spring constant is 65 N/m. What is the cube’s launch speed as it leaves the spring? Assume that the surface is frictionless.

Answer 51

3.1 m/s

Question 52

Stop to Think 9.8
A block is attached to a spring, the spring is stretched, and the block is released at the position shown. As the block moves to the right, is the work done by the wall positive, negative, or zero?

Answer 52

Zero. The wall exerts a force on the right end of the spring, but the point of application does not move.

Question 53

how quickly the energy is transferred ?

Answer 53

So when we raise the issue of how quickly the energy is transferred, we are talking about the rate of transfer of energy. The rate at which energy is transferred or transformed is called the power P, and it is defined as

P=F ⋅v =Fvcosθ

Question 54

unit of power ?

Answer 54

watt

Question 55

Example 9.11 Power output of a motor
A factory uses a motor and a cable to drag a 300 kg machine to the proper place on the factory floor. What power must the motor supply to drag the machine at a speed of 0.50 m/s? The coefficient of friction between the machine and the floor is 0.60.

Answer 55

882W

Question 56

Example 9.12 Power output of a car engine
A 1500 kg car has a front profile that is 1.6 m wide by 1.4 m high and a drag coefficient of 0.50. The coefficient of rolling friction is 0.02. What power must the engine provide to drive at a steady 30 m/s (≈ 65 mph) if 25% of the power is “lost” before reaching the drive wheels?

Answer 56

51 hp

Question 57

Stop to Think 9.9
Four students run up the stairs in the time shown. Rank in order, from largest to smallest, their power outputs Pa to Pd.

Answer 57

book

Question 58

Example 9.13 Stopping a brick
A 25.0-cm-long spring stands vertically on the ground, with its lower end secured in a base. A 1.5 kg brick is held 40 cm directly above the spring and dropped onto the spring. The spring compresses to a length of 17.0 cm before starting to launch the brick back upward. What is the spring’s spring constant?

Answer 58

2200 N/m