Energy

Unit 5: Energy and Work

Energy

Mechanical Energy

• Mechanical energy is energy due to the motion of an object
• There are two types of mechanical energy:
• Kinetic energy
• Potential energy

1. Kinetic Energy: energy associated with an object in motion – always positive

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Which point has the MOST kinetic energy?

Which point has the LEAST kinetic energy?

1. Kinetic Energy:

KE = ½mv² m = mass v = velocity (or speed)

Sample Problem 1: A child, m = 34 kg, runs with a velocity of 1.75 m/s. what is the child’s kinetic energy?

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Sample Problem 2: A 500 kg horse has a kinetic energy equal to 7840 J. How fast is the horse moving?

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KE = ½mv²

KE = ½(34)(1.75²)

KE = 52 J

KE = ½mv²

7840 = ½(500)(v²)

7840 = 250v²

31.36 = v²

v = 5.6 m/s

2. Potential Energy: “stored” energy
1. Gravitational Potential Energy: energy associated with an object due to the position of the object relative to the Earth or some other gravitational source
• Can be positive or negative based on your point of reference

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Which point has the MOST GPE?

Which point has the LEAST GPE?

2. Potential Energy: “stored” energy
1. Gravitational Potential Energy:

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PE = mgh m = mass g = gravity (9.8 m/s²⁾ h = height

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Sample Problem: What is the gravitational potential energy of a 10 kg cat resting atop a 2.3 m refrigerator?

GPE = mgh

GPE = (10)(9.8)(2.3)

GPE = 225.4 J

2. Potential Energy: “stored” energy

• Elastic Potential Energy: energy stored as a result of applying a force to deform the object (stretching, compressing, twisting, etc.)
• Energy is stored until the object springs back to its original shape

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Total Mechanical Energy

• Total mechanical energy is the sum of the potential and kinetic energy

TME = KE + PE

Lesson Check 5.2

LAW OF CONSERVATION OF ENERGY

Unit 5: Energy & Work

Open vs Closed System

• You are boiling water on the stove in two separate pots. One of these has a lid and one is open.
• Which of these do you think is a closed system? An open system?

OPEN

CLOSED

Open vs Closed System

Applying this to the law of conservation of energy:

• A system is an object or collection of objects that interacts (ex. A planet, liquid within a glass, etc.)
• In a closed system, energy can only be transferred within the system (ex. Ice in a bag doesn’t let water escape)
• Closed systems are imaginary, but we often use them to calculate “perfect” conditions
• In an open system, energy can be transferred with the surroundings (ex. Car motor, a car accelerating on the road, etc.)

Open vs Closed System

If the system is closed, and there are no friction or other energy-loss processes, the amount of mechanical energy described in a problem must be constant

The Law of Conservation of Energy

• States: Energy can never be created or destroyed but can change from one form to another

The Law of Conservation of Energy

• Consider a ball thrown straight up:
• the ball leaves your hand with KE
• as it goes higher, it loses KE and gains PE
• at the very top, the ball will have all PE and zero KE
• once the ball begins to fall down, the ball loses PE and gains KE

On the way up, the ball is losing speed

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KE is decreasing

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PE is increasing

Ball is stationary

KE = 0

PE is greatest

On the way down, the ball is gaining speed

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KE is increasing

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PE is decreasing

BASICALLY

The total mechanical energy at one moment is equal to the total mechanical energy at another moment

Energy Bar Charts

KE_i + PE_i = TME

KE_f + PE_f = TME

Energy Bar Charts

Total Mechanical Energy stays the same, but the motion/location of the object determines how much KE and PE there is at a given point.

Law of Conservation of Energy Formula

Sample Problem 1

A. Match the energy bar chart with the correct position of the skateboarder.

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Sample Problem 1

B. Where on the path would the skateboarder represent chart 4?

Sample Problem 2

Astro, a cat whose mass is 5.45 kg, is napping on top of the refrigerator when he rolls over and falls. Astro has a KE of 85.5 J just before he lands on his feet on the floor. How tall is the refrigerator?

m = 5.45 kg

KE = 85.5 J

h = ?

ME_i = ME_f

PE_i + KE_i = PE_f + KE_f

at rest, no KE

on the floor, no PE

PE_i = KE_f

mgh = KE_f

(5.45)(9.8)h = 85.5

53.41h = 85.5

h = 1.6 m

Sample Problem 3

A 20-kg rock sits on the edge of a cliff. The height of the cliff is 100 m. What will be the speed of the rock before landing?

m = 20 kg

KE = ?

h = 100 m

ME_i = ME_f

PE_i + KE_i = PE_f + KE_f

at rest, no KE

on the floor, no PE

PE_i = KE_f

mgh = ½mv²

(20)(9.8)(100) = ½(20)v²

19600 = 10v²

1960 = v²

v = 44.3 m/s

Sample Problem 4

Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300 kg hot dog cart rolls down Nob Hill and reaches point A (h=50 m) at a speed of 8 m/s. How fast is the hot dog cart going at point B (h=30.0 m) when Frank finally wakes up and starts to run after it?

A

B

h_i = 50m v_i = 8 m/s

h_f = 30m v_f = ??

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ME_i = ME_f

PE_i + KE_i = PE_f + Ke_f

mgh_i + ½mv_i² = mgh_f + ½mv_f²

(300)(9.8)(50) + ½(300)(8²) = (300)(9.8)(30) + ½(300)v_f²

147,000 + 9,600 = 88,200 + 150v_f²

156,600 = 88,200 + 150v_f²

68,400 = 150v_f²

456 = v_f²

v_f = 21.4 m/s

Lesson Check 5.3