How Force, Power, Torque and Energy Work
To discuss all this we need to know that
What is Mass?
Generally, mass is defined as the measure of how much matter an object or body contains -- the total number of subatomic particles (electrons, protons and neutrons) in the object. If you multiply your mass by the pull of Earth's gravity, you get your weight. So if your body weight is fluctuating, because of eating or exercising, it is actually the number of atoms that is changing.
It is important to understand that mass is independent of your position in space. Your body's mass on the moon is the same as its mass on Earth, because the number of atoms is the same. The Earth's gravitational pull, on the other hand, decreases as you move farther away from the Earth. Therefore, you can lose weight by changing your elevation, but your mass remains the same. You can also lose weight by living on the moon, but again, your mass is the same.
What is Force?
One type of force that everyone is familiar with is weight. This is the amount of force that the Earth exerts on you. There are two interesting things about this force:
- It pulls you down, or, more exactly, toward the center of the Earth.
- It is proportional to your mass. If you have more mass, the Earth exerts a greater force on you.
When you step on a bathroom scale, you exert a force on the scale. The force you apply to the scale compresses a spring, which moves the needle. When you throw a baseball, you apply a force to the ball, which makes it speed up. An airplane engine creates a force, which pushes the plane through the air. A car's tires exert a force on the ground, which pushes the car along.
Force causes acceleration. If you apply a force to a toy car (for example, by pushing on it with your hand), it will start to move. This may sound simple, but it is a very important fact. The movement of the car is governed by Isaac Newton's Second Law, which forms the foundation for classical mechanics. Newton's Second Law states that the acceleration (a) of an object is directly proportional to the force (F) applied, and inversely proportional to the object's mass (m). That is, the more force you apply to an object, the greater the rate of acceleration; and the more mass the object has, the lower the rate of acceleration. Newton's Second Law is usually summarized in equation form:
a = F/m, or F = ma
Unit of Force
To honor Newton's achievement, the standard unit of force in the SI system was named the newton. One newton (N) of force is enough to accelerate 1 kilogram (kg) of mass at a rate of 1 meter per second squared (m/s2). In fact, this is really how force and mass are defined.
What is Torque?
Torque is a force that tends to rotate or turn things. You generate a torque any time you apply a force using a wrench. Tightening the lug nuts on your wheels is a good example. When you use a wrench, you apply a force to the handle. This force creates a torque on the lug nut, which tends to turn the lug nut.
English units of torque are pound-inches or pound-feet; the SI unit is the Newton-meter. Notice that the torque units contain a distance and a force. To calculate the torque, you just multiply the force by the distance from the center. In the case of the lug nuts, if the wrench is a foot long, and you put 200 pounds of force on it, you are generating 200 pound-feet of torque. If you use a 2-foot wrench, you only need to put 100 pounds of force on it to generate the same torque.
A car engine creates torque and uses it to spin the crankshaft. This torque is created exactly the same way: A force is applied at a distance. Let's take a close look at some of the engine parts:
Diagram
How torque is generated in one cylinder of a four-stroke engine
The combustion of gas in the cylinder creates pressure against the piston. That pressure creates a force on the piston, which pushes it down. The force is transmitted from the piston to the connecting rod, and from the connecting rod into the crankshaft. In Figure 2, notice that the point where the connecting rod attaches to the crank shaft is some distance from the center of the shaft. The horizontal distance changes as the crankshaft spins, so the torque also changes, since torque equals force multiplied by distance.
You might be wondering why only the horizontal distance is important in determining the torque in this engine. You can see in Figure 2 that when the piston is at the top of its stroke, the connecting rod points straight down at the center of the crankshaft. No torque is generated in this position, because only the force that acts on the lever in a direction perpendicular to the lever generates a torque.
What is Work?
The work we are talking about here is work in the physics sense. Not home work, or chores, or your job or any other type of work. It is good old mechanical work.
Work is simply the application of a force over a distance, with one catch -- the distance only counts if it is in the direction of the force you apply. Lifting a weight from the ground and putting it on a shelf is a good example of work. The force is equal to the weight of the object, and the distance is equal to the height of the shelf. If the weight were in another room, and you had to pick it up and walk across the room before you put it on the shelf, you didn't do any more work than if the weight were sitting on the ground directly beneath the shelf. It may have felt like you did more work, but while you were walking with the weight you moved horizontally, while the force from the weight was vertical.
Your car also does work. When it is moving, it has to apply a force to counter the forces of friction and aerodynamic drag. If it drives up a hill, it does the same kind of work that you do when lifting a weight. When it drives back down the hill, however, it gets back the work it did. The hill helps the car drive down.
Work is energy that has been used. When you do work, you use energy. But sometimes the energy you use can be recovered. When the car drives up the hill, the work it does to get to the top helps it get back down. Work and energy are closely related. The units of work are the same as the units of energy, which we will discuss later.
What is Power?
Power is a measure of how quickly work can be done. Using a lever, you may be able to generate 200 ft-lb of torque. But could you spin that lever 3,000 times per minute? That is exactly what your car engine does.
The SI unit for power is the watt. A watt breaks down into other units that we have already talked about. One watt is equal to 1 Newton-meter per second (Nm/s). You can multiply the amount of torque in Newton-meters by the rotational speed in order to find the power in watts. Another way to look at power is as a unit of speed (m/s) combined with a unit of force (N). If you were pushing on something with a force of 1 N, and it moved at a speed of 1 m/s, your power output would be 1 watt.
An interesting way to figure out how much power you can output is to see how quickly you can run up a flight of stairs.
- Measure the height of a set of stairs that takes you up about three stories.
- Time yourself while you run up the stairs as quickly as possible.
- Divide the height of the stairs by the time it took you to ascend them. This will give you your speed.
For instance, if it took you 15 seconds to run up 10 meters, then your speed was 0.66 m/s (only your speed in the vertical direction is important). Now you need to figure out how much force you exerted over those 10 meters, and since the only thing you hauled up the stairs was yourself, this force is equal to your weight. To get the amount of power you output, multiply your weight by your speed.
Power (W) = (height of stairs (m) / Time to climb (s) ) * weight (N)
Power (hp) = [(height of stairs (ft) / Time to climb (s) ) * weight (lb)] / 550
Kinetic Energy
Kinetic energy is energy of motion. Objects that are moving, such as a roller coaster, have kinetic energy (KE). If a car crashes into a wall at 5 mph, it shouldn't do much damage to the car. But if it hits the wall at 40 mph, the car will most likely be totaled.
Kinetic energy is similar to potential energy. The more the object weighs, and the faster it is moving, the more kinetic energy it has. The formula for KE is:
KE = 1/2*m*v2
where m is the mass and v is the velocity.
One of the interesting things about kinetic energy is that it increases with the velocity squared. This means that if a car is going twice as fast, it has four times the energy. You may have noticed that your car accelerates much faster from 0 mph to 20 mph than it does from 40 mph to 60 mph. Let's compare how much kinetic energy is required at each of these speeds. At first glance, you might say that in each case, the car is increasing its speed by 20 mph, and so the energy required for each increase must be the same. But this is not so.
We can calculate the kinetic energy required to go from 0 mph to 20 mph by calculating the KE at 20 mph and then subtracting the KE at 0 mph from that number. In this case, it would be 1/2*m*202 - 1/2*m*02. Because the second part of the equation is 0, the KE = 1/2*m*202, or 200 m. For the car going from 40 mph to 60 mph, the KE = 1/2*m*602 - 1/2*m*402; so KE = 1,800 m - 800 m, or 1000 m. Comparing the two results, we can see that it takes a KE of 1,000 m to go from 40 mph to 60 mph, whereas it only takes 200 m to go from 0 mph to 20 mph.
There are a lot of other factors involved in determining a car's acceleration, such as aerodynamic drag, which also increases with the velocity squared. Gear ratios determine how much of the engine's power is available at a particular speed, and traction is sometimes a limiting factor. So it's a lot more complicated than just doing a kinetic energy calculation, but that calculation does help to explain the difference in acceleration times.
Bringing it Together
Now that we know about potential energy and kinetic energy, we can do some interesting calculations. Let's figure out how high a pole-vaulter could jump if he had perfect technique. First we'll figure out his KE, and then we'll calculate how high he could vault if he used all of that KE to increase his height (and therefore his PE), without wasting any of it. If he converted all of his KE to PE, then we can solve the equation by setting them equal to each other:
1/2*m*v2 = m*g*h
Since mass is on both sides of the equation, we can eliminate this term. This makes sense because both KE and PE increase with increasing mass, so if the runner is heavier, his PE and KE both increase. So we'll eliminate the mass term and rearrange things a little to solve for h:
1/2*v2 / g = h
Let's say our pole-vaulter can run as fast as anyone in the world. Right now, the world record for running 100 m is just under 10 seconds. That gives a velocity of 10 m/s. We also know that the acceleration due to gravity is 9.8 m/s2. So now we can solve for the height:
1/2*102 / 9.8 = 5.1 meters
So 5.1 meters is the height that a pole-vaulter could raise his center of mass if he converted all of his KE into PE. But his center of mass is not on the ground; it is in the middle of his body, about 1 meter off the ground. So the best height a pole-vaulter could achieve is in fact about 6.1 meters, or 20 feet. He may be able to gain a little more height by using special techniques, like pushing off from the top of the pole, or getting a really good jump before takeoff.
do you know that kinetic energy of wind can be converted to electrical energy using wind turbines
Wing with high speed and mass means that it has high amount of energy which is used to turn the blades of turbine antd the genrator convertes the enrgy of blades to electrical energy.
