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3.5 Calculating Energy

Site: Cowichan Valley School District - Moodle
Course: Science 10 with CSS teacher
Book: 3.5 Calculating Energy
Printed by: Guest user
Date: Saturday, 26 April 2025, 1:19 PM

Description

Work & Energy

Table of contents

Kinetic Energy

At this point we already know that kinetic energy is the energy of motion.

If an object has both mass and velocity, then it has kinetic energy.

We can calculate the kinetic energy of an object using:

begin mathsize 28px style E subscript k space equals space 1 half m v squared end style
Where,
  • m = mass of object (in kg)
  • v = velocity of object (in m/s)
  • Ek = kinetic energy (in Joules)

Energy in Lightning
A single lightning bolt unleashes the same energy as blowing up a ton of TNT.  Every day there are over eight million lightning strikes across the world. With the onset of global warming, that's expected to continue to rise. Each bolt superheats the air around it to about 54,000 degrees Fahrenheit - five times hotter than the sun.  Maybe someday we'll learn how to harness this energy.

Examples

Calculate the kinetic energy in each situation below:

Example #1:

locomotive

A 15000kg locomotive is moving at 20 m/s. What is its kinetic energy?

Give it a try before looking at solution.

Solution

Example #2:

running with parachute

David is in training and doing sprints with a parachute.  David and the parachute (together) have a mass of 75 kg and are travelling at 6.0 m/s.  What is the kinetic energy of the combo?

Give it a try before looking at the solution.

Solution

 

Example #3:

sling shot

Val releases a 50 gram bearing from her sling shot at 18 m/s.  What is the kinetic energy of the bearing?

Give it a try before looking at the solution.

Solution

Example #4:

pendulum

A 0.25 kg pendulum is swinging.   At the very top of its swing, it has no velocity (comes to a stop).   At the bottom of its swing, it has a velocity of 5.0 m/s.   What is the kinetic energy in each position?

Give it a try before looking at the solution.

Solution

Potential Energy

At this point we already know that potential energy is the energy of position.

Potential energy is often called "stored energy."

To have potential energy, an object must be part of a system that can apply force to the object.

We can calculate the potential energy of an object using:

begin mathsize 28px style E subscript p space equals space F subscript a v e end subscript d end style
Where,
  • Fave = average force on object (in Newtons)
  • d = distance over which force can be applied (in m)
  • Ep = potential energy (in Joules)

Examples

Calculate the increase in potential energy in the following examples.

Example #1:

bench press

Carol is bench pressing 85 kg (about 800N).   If each rep requires her to lift the bar about 1.0 m, how much potential energy does Carol increase the weights during a push up?

Give it a try before checking the solution.

Solution

Example #2:

sling shot

Val pulls back a bearing in her new sling shot.   She pulls it back about 30 cm with an average force of 100N.   What is the increase in potential energy caused by pulling it back?

Give it a try before checking the solution.

Solution

Example #3:

pendulum

A 0.5 N pendulum is swinging.   At the very top of its swing, it is 12 cm above its lowest position.   What is the difference in potential energy between lowest and highest positions?

Give it a try before looking at the solution.

Solution

Gravitational Potential Energy

To have potential energy, an object must be part of a system that can apply force to the object.

We may not think of it, but the Earth is part of a system creating potential energy for all masses on it's surface. 

Thus, the most common potential energy that we experience is gravitational potential energy.

We can calculate the gravitational potential energy of an object using:

begin mathsize 28px style E subscript p space equals space m g h end style
Where,
  • m = the mass of the object (in kg)
  • g = gravitational constant for the surface of Earth (in m/s2)
  • Ep = potential energy (in Joules)
  • note that "mg" together make the force of gravity (in Newtons)

Examples

In the following situations, calculate the increase in potential energy.

Example #1:

picking up box

What is the increase in potential energy cause by lifting a 50 kg box to a height of 1.5m?  

What would be the change in potential energy if he drops the box to the floor?

Give it a try before checking the solution.

Solution

Example #2:

picking up rock

A rock of mass 4.7 kg is lifted from height 2.1 m to 3.0 m. How much of an increase in potential energy was caused?

Give it a try before checking the solution.

Solution

 

Example #3:

moving box

If a person carries a 20 kg box from one shelf to another (same height but 3 m away), what was the change in potential energy? 

Think about an answer before checking the solution.

Solution

Example #4:

roller coaster

At the first stage of a roller coaster ride, the 1500kg roller coaster ends up 40 m above its starting height.   What was increase in potential energy of the roller coaster?

Give it a try before checking the solution.

Solution

Overview Video

You'll know all of this now, but it's a good review of your knowledge to this point

Interview

What do physicists, technologists, and engineers do? Here's an example.