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The lesson will cover the basics of energy, work, power, and momentum.
Energy is everywhere around us. It is a fundamental quantity that all physical systems contain in one form or another. The concept of energy is not difficult to understand. Energy is a quantity that can be moved or transferred from one place or from one form to another, and like mass, it cannot be created or destroyed. The simplest way to define energy is that energy is the ability to do work. All energy and work can be interconverted between actual work done, potential energy, and kinetic energy. Energy is also defined as the amount of work required to change the state of a physical system (e.g., from liquid to gas) Potential energy is sometimes called “stored energy.”
Here are some of the ways that energy is stored:
How do we change energy between its various forms? Sometime this occurs naturally, as when an object falls toward the earth. “working.” Work is done when energy is transferred from one place to another. More specifically, the amount of work done equals the amount of transferred energy. Here are a few examples of when work is done:
In a parallel fashion, energy can be transferred from one form of storage into another. Using the examples from above, the electromotive force in a battery enables the energy to transfer from chemical energy to radiant and heat energies in the circuit. Similarly, the gravitational force enables energy to transfer from potential energy into kinetic and heat energies through the turning of a water wheel.
How would you explain the operation of a car in terms of energy and work? Think about all the ways that energy is converted, used, and stored during the car’s operation. Also consider how forces enable the energy to transfer from one mode into another. Click on the following link to check your explanation:
Chemical energy is stored as chemical bonds in the gasoline. When gasoline combusts, the liquid is changed to a gas through combustion, and the gas expands to do work on the pistons. The pistons transfer the energy into kinetic energy that turns the drive shaft and the tires. The frictional force between the tires and the road transfers that kinetic energy to the kinetic energy of the car. Hence, the car moves.
How do we calculate work? When objects are moved, work is done when the applied force is in the same direction that the object will be moved. Motion in any other direction than the proposed direction of motion does not count toward the work being done. For example, when an object is lifted vertically, work (W) is calculated by taking the product of the force applied (F) and height that it is lifted (h). In this case the height the object is lifted against gravity becomes the distance, and the work is called “gravitational work.” Thus the normal work equation Work = force(f) x distance(d) becomes:
W = F h
The force that we’re lifting against is, of course, the gravitational force. This force is calculated by taking the product of an object’s mass (m) times the strength of the gravitational field (g = 9.8 N/kg on the surface of the earth). So, our equation becomes:
Work = m g h
For example, how much work would it take to lift a 40 kg barbell to a height of 2 meters from the ground?
W = m g h = 40 kg · (9.8 N/kg) · 2 m = 784 J
Note: m x g is the weight of an object
Practice Question: How much work would it take to carry the same barbell 5 meters across the room?
The correct answer is C. No work is done because the applied force (gravity in this case) is not in the direction of the motion. The calculation looks like this: W = mgh = 40 kg · (9.8 N/kg) · 0 m = 0 J
Sometimes we don’t have the physical strength or mechanical power to apply enough force to get a job done. Simple machines are devices that make work easy. They can help us by changing the direction of the applied force, reducing the magnitude of the input force, or helping to add speed to the rate at which work is done. This sounds almost magical, like we’re getting something from nothing. But, alas, the law of energy conservation still governs the universe. Reduced forces applied through simple machines are a consequence of increasing distances. For example, the equation
Work in = Work out
(F d) in = (F d ) out
Where F = force, and d = distance, the formula shows how an ideal machine transfers no energy to heat by frictional forces, since “work in” equals “work out.”
A classic example, the lever, can significantly reduce the input forces and yield large output forces. The handle is easily moved over a large distance and an object is pried through a small distance as shown in the following figure:
(F d) in = (F d ) out
The mechanical advantage (MA) of a simple machine is the ratio between the output force (F out) to the input force (F in):
(F d) in = (F d ) out
F ·13m = 130N · 5m
F = 50 N
Pulleys, wedges, ramps, and screws are some other examples of simple machines that offer a mechanical advantage. It is a good exercise to think about how these simple machines save us work in our everyday lives.
What is the relationship between energy, work, and power? Power (P) is the rate at which work is done. For example, 100-Watt light bulb uses twice as much energy in a second as a 50-Watt light bulb. The following equation can be used to calculate power:
To calculate the power output of a 150N child that climbs 5 meters up a rope in 10 seconds, the following calculation is made:
Who is more powerful: a man who lifts a 200-N barbell 2 meters vertically in 2 seconds, or a boy who lifts a 100-N barbell 1 meter in 0.5 seconds?
They both have the SAME power:
Like energy and mass, the momentum of a system is also conserved. Momentum (p) is a product of an object’s mass (m) and its velocity (v):
p = m v
In other words, momentum is a product of a mass in motion. Momentum also has direction associated with it and is considered a vector. For example, we can calculate the momentum of a 2000 kg car heading north at a speed of 20 m/s.
p = m v = 2000kg · 20 m/s = 40,000 kg m/s north
But what about momentum being conserved? This concept is a consequence of Newton’s second law and can be written as:
Fnet = mΔv / Δt = Δp
or Fnet(Δt)= m(Δv) = Δp
Fnet is the net force of the system, Δv is the change in velocity, Δt is the change in time, and Δp is the change in momentum. The term Fnet (Δt) is called impulse, and is exactly the same quantity as m(Δv) . It gives us another way to view momentum.
If there is no net force applied to a system, then this implies that Δp is zero. In other words, with no unbalanced force on a system there is no momentum change.
For example, consider a billiard ball moving at 2 m/s that squarely strikes an identical billiard ball that’s at rest. The moving ball stops and the momentum is completely transferred to the other ball, which picks up a speed of 2 m/s. Momentum is NOT conserved for the first billiard ball alone because it experiences a net force. Momentum IS conserved for the SYSTEM of both balls because the collision forces are internal to the system.
What if two objects of different masses collide? For example, what if a 2000-kg boxcar moving at 30 m/s hits and links with a 1000-kg boxcar that’s initially at rest? How fast does the combination move after the collision? To answer this, we must note that the amount of moving mass increases after the collision. This means that the speed of the system must decrease so that the momentum is conserved.
