Kim Woods only

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 1: Magnitudes and Directions The magnitude of a physical quantity is the resulting value of a measurement or calculations of a quantity. This value is always expressed as the product of a number and specific unit measurement for this quantity.

Magnitudes allow us to compare the values of the same physical quantities. We know that a bus weighs more than a car because the magnitude of the bus’s weight is greater than the magnitude of the car’s weight.

Scalars are quantities that are completely defined by their magnitude.

For example:

The temperature in the room is 23 degrees Celsius.

The mass of the sumo wrestler is 170 kg.

Vectors are quantities that are defined by specifying both magnitude and direction. Vector quantities are often represented by arrows that point in the direction of the motion or action. Some examples of vector quantities are velocity, acceleration, force, and momentum.

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MOTION

Scalars do not have direction!

COURSE NOTES - PART 1

A"bus" (12"tons)"

A"car" (1.5"tons)"

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Parallel Vectors are vectors that are acting in the same direction. Both will be represented as positive magnitudes.

Antiparallel Vectors are vectors that are acting in opposite directions. One will be represented as a positive magnitude and the other a negative magnitude.

A dimension is a number used to locate a position in space or an object.

The dimensions of a space or object is the numbers (coordinates) required to locate a position in that space or object.

On a line, only one coordinate is required to locate a position. A line, therefore, is a one-dimensional object.

On a surface, two coordinates are required to locate a position. A surface, therefore, is a two-dimensional object.

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1 2

3

0 mile 1 mile 2 miles 3 miles

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Distance is a measurement in one dimension.

If an object moves from one position to another, then the distance between those two positions can be referred to as the change in position.

Area is a measurement in two directions. Area is measured in units of a square that has a standard unit of length as a side.

Volume is a measurement in three directions.

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1

Common Distance Units: inches (in), feet (ft), centimeters (cm), meters (m).

2 Common Area Units: square inches (in2), square feet (ft2), square centimeters (cm2)

3 Common Volume Units: cubic inches (in3), cubic feet (ft3), cubic centimeters (cm3), Liters (L)

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 2: Speed, Velocity, and Acceleration The concept of speed is familiar to most people because riding in cars is a common activity in our daily lives. When you are describing how fast something is moving, you are referring to the object’s speed.

Velocity is another term that is often used to describe how fast an object is moving. The terms “speed” and “velocity” are often used interchangeably in everyday conversation, but there is an important distinction between the two in scientific language. Speed is a scalar quantity that describes how fast an object is moving without regard to the direction of motion. Velocity is a vector quantity that describes how fast an object is moving and which direction the object is moving.

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Speed is a scalar quantity, so it only needs the magnitude, or the value, in order to be fully

defined.

Velocity is a vector quantity, so it requires the magnitude and direction in order to be fully

defined.

10 mph

30 mph65 mph

10 mph

30 mph65 mph

South

Southwest West

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Velocity can be calculated by dividing the distance traveled by the time.

Example: What is the velocity of a car that travels 150 meters East in 2 seconds?

Note: The following step-by-step process can be used for every calculation problem in this class!

Step 1: Define what you know.

TIP: Look for the numbers (or magnitudes) and units!

What is the velocity of a car that travels 150 meters East in 2 seconds?

So we know that: d = 150 meters and t = 2 seconds.

Step 2: Figure out what you are solving for.

What is the velocity of a car that travels 150 meters East in 2 seconds?

So we know that we are solving for velocity: v = ?

Step 3: Decide which equation to use.

TIP: Look at your list of variables from Steps 1 and 2 (velocity, v; distance, d; time, t). Then, refer to the equation sheet to see if you can find an equation with those variables!

Step 4: Place values from Step 1 into the equation.

Step 5: Solve!

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v = d t

v = velocity (m/s) d = distance (m) t = times (s)

v = d t

v = d t

v = 150 m

2 s v = 75 m/s East

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Acceleration is also a familiar concept. We generally use the term in our everyday lives to describe an object that is speeding up. And while this is partially correct, the scientific definition of acceleration is the rate at which velocity changes. This means that an accelerating object can be speeding up, slowing down, or even turning (a change in direction also changes the velocity, since velocity is a vector quantity!).

Acceleration can be calculated by dividing the change in velocity by the time.

Example #1: Positive Acceleration (Speeding Up)

An object goes from rest to 50 m/s in 10 seconds. What acceleration is the object experiencing?

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Positive acceleration means an object is speeding up.

Negative acceleration means an object is slowing down.

Zero acceleration means an object is either at rest or moving at a constant velocity.

a = vf −vi t

a = acceleration (m/s2) vf = final velocity vi = initial velocity t = time (s)

a = vf −vi t

a = 50 m/s - 0 m/s

10 s

a = 50 m/s 10 s

a = 5 m/s2

This means that the object increases its

speed by 5 m/s every second!

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Example #2: Negative Acceleration (Slowing Down)

A car traveling at 30 m/s crashes into a wall and stops in 0.1 seconds. What acceleration is the car experiencing?

We have a special acceleration on Earth called the acceleration of gravity, or gravitational acceleration. This acceleration is a uniform acceleration, which occurs whenever there is a constant force acting on an object. The acceleration of gravity on Earth is 9.8 m/s2. This means that falling objects on Earth increase their speed by 9.8 m/s every second. This number is a constant on Earth due to gravity from Earth’s mass.

If Earth was more massive, objects would accelerate at a faster rate towards the surface. Similarly, if Earth was less massive, objects would accelerate at a slower rate towards the surface.

For example, the Moon is 81 times less massive than

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Total Distance Traveled

Relates to Velocity Relates to

Acceleration

a = vf −vi t

a = 0 m/s - 30 m/s

0.1 s

a = −30 m/s

0.1 s a = −300 m/s2

This means that the object decreases its

speed by 300 m/s every second!

Industry Connection: Have a strong understanding of velocity and acceleration is important for being able to give a realistic and accurate feel to moving objects in simulations and animations. Each frame of your animation is a set amount of time so the “speed” of the moving object will be based on how far the object has moved between frames. v=d/t so v x t=d . The further the object travels between each frame the faster the object is moving.

Acceleration is how quickly velocity is changing, so for an animation, changing the distance the object moves between different each frame will represent acceleration. An exaggerated example, an object moves 1cm between frame 26 and frame 27, but the object only moves 0.5 cm between frame 27 and frame 28. This would mean the object experienced negative acceleration (slowed down) during this time.

A constant force will produce a constant acceleration and thus will change the distance covered between each frame the same amount. Say you wanted to animate something falling, which causes a constant acceleration. Depending on frame speed and where the object is in your scene you will have something similar to this:

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

the Earth, so all objects on the Moon fall at a rate of 1.622 m/s2.

Whereas Jupiter is 318 times more massive than Earth, so all objects on Jupiter accelerate at a rate of 24.5 m/s2.

Section 3: Forces Force is defined as a push or a pull on an object that causes a change in an object’s velocity. Forces can be divided into two categories: contact forces and action-at-a-distance forces. Contact forces are forces that cause a change in velocity by two objects physically touching one another. If you push a shopping cart down the aisle at the grocery store, that is an example of a contact force. Action-at-a-distance forces are forces where the objects involved do not need to be physically touching each other in order for them to affect each other’s velocities. An example of this would be gravitational force. The Earth orbits around the Sun due to the gravitational pull of the Sun, but the two celestial bodies do not physically touch each other.

Force can be calculated by multiplying the mass of the object times the acceleration.

Example #1

How much force is required to accelerate a 50 kg object 5 m/s2?

Example #2

What is the acceleration of a 25 kg object if pushed with a force of 100 N?

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F = ma F = force (N) m = mass (kg) a = acceleration (m/s2)

F = ma F = (50 kg)(5 m/s2 )

F = 250 N

F = ma 100 N = (25 kg)a

a = 100 N 25 kg

a = 4 m/s2

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Example #3

What is the mass of an object that is accelerating at 3 m/s2 with a force of 60 N applied?

Net Force is the sum of all forces (ƩF) that act on an object. Anytime the net force on an object is NOT equal to zero, the object will experience an acceleration.

Parallel force vectors are added.

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F = ma 60 N = m(3 m/s2 )

m = 60 N

3 m/s2

m = 20 kg

ƩF = 200 N + 100 N = 300 N

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Antiparallel force vectors are subtracted.

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ƩF = 900 N - 500 N = 400 N

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

The first step to predicting the motion of an object is to identify the forces acting on that object.

For a person pushing a box across the floor, the following forces exist:

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

An object experiences static equilibrium at a state of rest.

An object experiences dynamic equilibrium while moving at constant velocity.

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 4: Mass, Weight, and Inertia Here is another case where the terminology used in our everyday lives slightly varies from the scientific definitions. In normal conversation, we may use the terms “mass” and “weight” interchangeably. In physical science, however, these terms have very different meanings. An object’s mass is a scalar quantity that describes the amount of matter that an object contains and is measured in kilograms (kg). An object’s weight is a vector quantity that describes the amount of gravitational force upon an object and is measured in Newtons (N).

Mass will not change when the gravitational environment changes. The weight, however, will change when gravity changes.

Weight is a specific type of force that is caused by gravity pulling by a mass and can be calculated by multiplying the mass times the acceleration of gravity.

Inertia is an object’s natural resistance to change. An object has a tendency to maintain its state of motion unless an outside force acts on the object. This means that an object at rest will stay at rest unless an outside force acts on that object. This also means that an object in motion will stay in motion unless an outside force acts on that object. Any object with mass has inertia. The more massive the object, the greater the amount of inertia and the greater amount of force that is required to change the object’s state of motion. Likewise, the less massive the object, the smaller amount of inertia and the smaller amount of force that is required to change the object’s state of motion.

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w = mg w = weight (N) m = mass (kg) g = acceleration due to gravity (m/s2)

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 5: Newton’s Laws of Motion Isaac Newton (1642-1727) proposed a theory of the causes of motion that could explain the motion of any object, whether it be an ordinary Earthbound object or the motion of celestial objects. Before Newton, celestial and Earthbound movements were treated completely independent of each other and were thought to behave by different laws. Newton’s theory did away with the distinction between the two types of motion. Newton’s theory consists of three laws of motion and his universal law of gravitation (to be discussed in week 4). The following discussion of his laws will build on the concepts of inertia, mass, and forces previously discussed in Section 3.

Objects have inertia from their mass, so they resist any change to their velocity. A force is required to accelerate (change the velocity of) objects.

Real World Examples of Newton’s First Law

• Blood rushes from your head to your feet when quickly stopping on a descending elevator. When descending, everything in your body is moving downward at the same speed as the elevator. When the elevator stops, the force is applied to your feet to make it stop, but no force is applied to the blood inside your body and the blood will rush downward to your feet.

• A brick is broken painlessly over a person’s hand with a hammer. The more massive an object, the more inertia it has and the greater force is required to take that object out of its state of motion. When the brick is at rest, it wants to stay at rest. When the force of the hammer is applied, the inertia of the brick resists the change in motion toward your hand, and your hand is left relatively unharmed.

• Headrests are installed in cars to prevent whiplash injuries during rear-end collisions because your head will tend to stay at rest while the cars and the rest of your body moves forward. This results in a very quick snapping of the neck backwards relative to the rest of your body, even though in actuality your head is simply trying to stay at rest.

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Newton’s First Law (The Law of Inertia)

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

ForceVelocity X Velocity Y

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

• While riding a bicycle, you fly forward off your bicycle when hitting an object that stops the motion of the bicycle because the force was not applied to your body as well. So your body will continue forward in a straight line at the same speed the bicycle was moving until gravity takes over (another external force) and you fall to the ground.

• Coffee spills in a car when accelerating or decelerating quickly. If the car is initially at rest, then the coffee is also at rest. When the car suddenly speeds up, the coffee’s inertia wants it to stay at rest, so it will likely spill backwards onto your lap. If the car was initially in motion, then the coffee is also in motion at the same speed and in the same direction as the car. If the car suddenly stops, the coffee stays in motion by its inertia and will likely spill forward onto your dashboard.

Newton’s Second Law can be broken down into two parts.

Part 1: The acceleration produced by a net force on an object is directly proportional to the net force and in the same direction as the net force.

This means that the greater the net force on an object, the greater its acceleration. This also means that an object’s net force vector and its acceleration vector are parallel.

Part 2: The acceleration produced by a net force on an object is inversely proportional to the mass of the object.

Since mass and acceleration are inversely proportional, the same force will have less acceleration (change in velocity) on an object with greater mass and greater acceleration on an object with less mass.

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Newton’s Second Law (The Law of Acceleration)

The acceleration produced by a net force on an object is directly proportional to the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Net Force

Same% Force%

Same% Force%

Greater% Mass%

Less% Mass%

Less Acceleration More Acceleration

Newton’s Third Law (Law of Action-Reaction)

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the force.

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Interacting objects always push against each other with the same magnitude of force and in opposite directions.

Newton’s Third Law may seem counterintuitive at first, but there are some important things to remember when considering this law.

1. We don’t see forces, we only see the results of forces, which is an acceleration.

2. Newton’s Second Law tells us that objects with lower mass will experience greater acceleration.

Let’s consider an example like a ball being dropped to the surface of the Earth. It might not seem like it is correct to say that the ball causes as much of a force on the Earth as the Earth has on the ball, but if we remember the two statements above, we can safely say that they are in equal in magnitude. We know that the acceleration is what we actually see, not the force, and will also be what balances the equation.

Section 6: Projectile Motion A projectile is any object that moves through air or through space only under the influence of gravity and air resistance. Air resistance is usually small enough for slow moving objects that we can ignore it. Examples of projectiles are soccer balls or golf balls in flight, but NOT airplanes or helicopters since they continue to apply force during flight. A parabola is the shape of the curved path of the projectile.

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Feet$push$on$ground$and$the$ ground$pushes$back$with$ same$force.7

Hands$push$on$the$ boulder$and$the$boulder$ pushes$back$with$same$ force.7

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Projectiles are launched with an initial force and velocity and then gravity takes over.

All projectiles have two things in common:

1. Constant Horizontal Motion: The speed the object moves across the ground (left or right) is constant and does not change.

2. Accelerated Vertical Motion: The speed in the vertical direction (up and down) is affected by gravity at a rate of 9.8 meters per second every second.

For projectiles, horizontal and vertical motion are independent of each other. Independent, meaning that neither motion affects the other.

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The yellow ball is shot at the same time the pink ball is released. The yellow ball’s horizontal motion does not affect its vertical motion. Both (yellow and pink) vertical motions are identical.

This means that if you drop a bullet and shoot another from the same height and at the same time, they reach the

ground at the same time!

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

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The Physics of Angry Birds Does the game follow correct projectile motion?

A program was used to track the path of an Angry bird as it soars across a level.

A straight line is formed when a graph of time and distance across the ground is made.

Horizontal speed is constant (as it should be).

Since the graph determined that horizontal speed was constant, we can conclude that the only force on the bird is gravity acting downward. A curved line is formed when a graph of

time and height above the ground is made.

Vertical speed is changing by gravity (as it should be).

Conclusion:

Angry Birds follows correct

projectile motion!

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

So, the rate an object is moving horizontally (across the Earth’s surface) does not affect the rate that it falls vertically (towards the Earth’s center).

Question #1:

An object at the edge of a cliff is shot horizontally with a speed of 10 m/s. Assume there’s no air resistance. If the object is still in flight, what is its horizontal speed 4 seconds after it is shot? How about 9 seconds after it is shot?

Answer #1:

Because a projectile always maintains a constant horizontal speed, its speed would still be 10 m/s regardless of time passed. At both times, the horizontal speed remains equal at 10 m/s.

Question #2:

An object at the edge of a cliff is shot horizontally with a speed of 10 m/s. Assume there’s no air resistance. If the object is still in flight, what is its vertical speed 2 seconds after it is shot?

Answer #2:

Because its vertical speed depends only on gravity and time (and it’s independent of the horizontal speed), the speed after two seconds would be:

The horizontal distance traveled by a projectile is called its range.

Two identical projectiles launched on level ground with the same initial speed will achieve the same range if they add up to 90 degrees. These are called complementary angles. Maximum range will be achieved at 45 degrees.

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vvertical = gt = (9.8 m/s 2 )(2 s) =19.6 m/s

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 7: Momentum, Work, and Power Momentum is the quantity of motion of a moving body, or inertia in motion. We use the word momentum in our everyday lives to describe an object or objects that are difficult to stop. A football team with a lot of momentum (metaphorically) is very difficult to beat or stop. This is essentially the definition of momentum in science as well - an object with a lot of momentum will be difficult to stop.

Momentum can be calculated by multiplying mass times velocity.

Momentum is directly proportional to mass, meaning that momentum of an object will increase as the mass of the object increases. Momentum is also directly proportional to velocity, meaning the momentum of an object will increase as the velocity of that object increases. Physically, a more massive object is harder to stop. An object moving faster is harder to stop. A massive object moving quickly is REALLY hard to stop!

Momentum is why an object with more mass applies a greater force than an object with less mass when it collides with a wall. A force is required to give momentum to an object, and a force is required to remove momentum from an object.

Example:

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MOMENTUM AND ENERGY

COURSE NOTES - PART 2

p = mv p = momentum (kgm/s) m = mass (kg) v =velocity (m/s)

Force! Momentum! Force!

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

How much momentum does a truck with a mass of 10,000 kg have if it is moving at 10 m/s?

Conservation (in general) means whatever amount you have before, you have the same amount after. A system will have the same amount of “something” both before and after any interaction occurs. Conservation of the rainforest is a perfect example. When loggers cut down a tree, they plant another one in order to conserve the rainforest.

The Conservation of Momentum states that in the absence of an external force, the momentum of a system during a collision remains unchanged.

An elastic collision occurs when objects collide and then bounce off each other without lasting deformation or the generation of heat. Billiard balls are a great example of an elastic collision. They collide, move away from one another, and do so without deforming or generating reasonable amount of heat.

Momentum is conserved in an elastic collision between two objects, so we can use the following equations for this specific case:

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p = mv p = (10, 000 kg)(10 m/s) p =100, 000 kgm/s

pbefore = pafter

The total momentum of the system (the two balls) remains the same in all three states.!

momentum of 1 = momentum of 2 = momentum of 3!

1. Before Collision!

2. During Collision! 3. After Collision!

pbefore = pafter (p1 + p2)before = (p1 + p2)after

(m1v1+m2v2)before = (m1v1+m2v2)after

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Example (Elastic Collision):

A 2-kg cart moving at 5 m/s runs into another 1-kg cart moving still. If the blue cart comes to a stop after the collision, what is the velocity of the red cart after the collision?

We must first find out the total momentum before the collision. This will be the momentum of the blue cart before the collision added to the momentum of the red cart before the collision.

So before the collision, the total momentum of the system is equal to 10 kgm/s + 0 kgm/s = 10 kgm/s. Because of the conservation of momentum, we know that this is also the total momentum after the collision. We can use this information to solve for the velocity of the red cart after the collision, as originally asked.

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€

p = mv

p = 2kg( ) 5m s( ) p =10kg⋅ m s

€

p = mv

p = 1kg( ) 0m s( ) p = 0kg⋅ m s

€

p = mv

p = 2kg( ) 0m s( ) p = 0kg⋅ m s

€

10 = mv 10 = 1kg( )*v v =10m s

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

A perfect inelastic collision occurs when objects collide, stick together, then continue moving attached to one another. Whenever an object is deformed in a collision, it is considered an inelastic collision as well.

Regardless of the type of collision, the Conservation of Momentum still applies:

Example (Inelastic Collision):

A cart of 500 kg moving at 10 m/s runs into another 500 kg cart sitting still. If they lock together, what is their velocity after the collision?

So before the collision, the total momentum of the system is equal to 5000 kgm/s + 0 kgm/s = 5000 kgm/s. Because of the conservation of momentum, we know that this is also the total momentum after the collision. We can use this information to solve for the velocity of the both carts after the collision, as originally asked. The difference this time will be that after the collision, both carts will stick together, so we need to add together the masses of the two carts before calculating the final velocity.

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pbefore = pafter

€

p = mv

p = 500kg( ) 10m s( ) p = 5000kg⋅ m s

€

p = mv

p = 500kg( ) 0m s( ) p = 0kg⋅ m s

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Work is done on an object when an applied force succeeds in moving the object over a distance. The unit of work is the Joule (J). You can think of work as adding or removing energy from something. There are three things that must occur in order for work to be done:

(i.) A force must be applied to an object,

(ii.) that object must be displaced from one position to another, and

(iii.) the force must be the cause of the displacement.

Work is calculated by multiplying force times distance.

Example (Horizontal Work):

How much work needs to be done to accelerate a 500 kg object 3 m/s2 to 2 meters?

Example (Vertical Work):

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€

p = (m1 + m2)vfinal 5000kg⋅ m s = 500kg + 500kg( )vfinal 5000kg⋅ m s = (1000kg)vfinal v final = 5m s

W = Fd W = Work (J) F = Force (N) d = distance (m)

W = Fd W = (ma)d

W = (500 kg)(3 m/s2 )(2 m) W = 3000 J

Since the problem does not state force directly, we will need to use the equation for force (F=ma) to ultimately solve for work.

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

How much work needs to be done to lift a 500-kg object to 2 meters height?

Power is the amount of work that is done per unit time. The unit of power is the Watt.

Example:

How much power is needed to accelerate a 2000-kg car 5 m/s2 a distance of 200 meters in 10 seconds?

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W = Fd W = wd

W = (mg)(d) W = (500 kg)(9.8 m/s2 )(2 m)

W = 9, 800 J

When lifting an object (vertical work), the force you need is the weight of the object (w=mg) because that is what you have to overcome in order for the object to move up.

P = W t

P = Power (W) W = Work (J) t = time (s)

P = W t

P = Fd t

P = (ma)d t

P = (2000 kg)(5 m/s2 )(200 m)

10s

P = 2, 000, 000 J

10 s P = 200, 000 W

We don’t know the value for work, so we have to solve for it (W=Fd).

We don’t know the value for force either, so we need another equation for that as well (F=ma).

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 8: Energy Energy produces changes in matter. Energy cannot be created or destroyed, only changed in form. The effects of energy are only observed when it is being transferred from one place to another or when it is transformed from one form to another. It is measured in Joules (J).

There are many types of energy, and many that you will learn about in this course. Some examples of types of energy are thermal energy (heat), acoustic energy (sound), magnetic energy (magnetic fields), electrical energy (electricity), mechanical energy (movement), and chemical energy (chemical bonds).

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Throughout energy transformations 1-4, the energy went from photonic to chemical to electrical to magnetic to acoustic. Energy is never lost, but just keeps changing!

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Potential Energy is defined as stored energy due to position, shape, or state. In its stored state, energy has the potential for doing work. An example of potential energy would be the energy stored in a drawn bow or a stretched rubber band.

Gravitational Potential Energy is the energy of an object due to the height of the object. When an object is lifted off of the surface of the Earth, it is being held away from something that it is attracted to. Once that restraint is released, the object will fall toward the surface of the Earth. Therefore, we say that the object has stored, or gravitational potential, energy, because it has the ability to do work when it is held to a height off of the ground.

Gravitational Potential Energy is calculated by multiplying mass times the acceleration of gravity times the height of the object.

Example:

How much potential energy does a 25 kg mass have when it is lifted to a height of 2 meters? How much work does it take?

The amount of work you did to lift the mass is the same as the amount of gravitational potential energy the object has. The work is what gave the ball the potential energy!

Kinetic Energy is the energy of a moving body. It is measured in Joules (J), and can be calculated by the following equation:

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height!

PE = mgh PE = Potential Energy (J) m = mass (kg) g = acceleration of gravity (m/s2) h = height (m)

PE = mgh PE = (25 kg)(9.8 m/s2 )(2 m)

PE = (245 N)(2 m) PE = 490 J

W = Fd W = wd = (mg)d

W = (25 kg)(9.8 m/s2 )(2 m) W = (245 N)(2 m)

W = 490 J

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Example:

How much kinetic energy does a 10-kg object have moving at 10 m/s?

The Conservation of Energy states that the energy of a system will remain constant, regardless of changes in form as long as there are no outside forces.

For a falling object, the gravitational potential energy at the top of the fall will transform entirely into kinetic energy by the end of the fall, but the Conservation of Energy states that the total amount of energy (kinetic + potential) will remain the same throughout the fall.

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KE = 1 2 mv2

KE = 1 2

(10 kg)(10 m/s)2

KE = (5 kg)(100 m 2 / s2 ) KE = 500 J

KE = Kinetic Energy (J) m = mass (kg) v = velocity (m/s)

KE = 1 2 mv2

Ebefore = Eafter

WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Example: A Falling Object

Total Energy = Kinetic Energy + Potential Energy

Let’s say that the total energy of the system is 10 Joules. This will not change throughout the fall because of the Conservation of Energy.

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WEEK 1 FUNDAMENTALS OF PHYSICAL SCIENCE

Another simple example of the Conservation of Energy is a swinging pendulum.

At the bottom, the bob has zero potential energy and maximum kinetic energy. At the left and right (highest) positions, the bob has zero kinetic energy and maximum potential energy.

For another example, consider the system of a bow and arrow. In drawing the bow, we do work on the system and give it potential energy. When the bowstring is released, most of the potential energy is transferred to the arrow as kinetic energy and some as heat to the bow.

Conservation of Energy shows itself all the time in our everyday lives!

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