Work relates to energy; whenever work is done, energy is transferred. It can change the amount of kinetic or potential energy an object has. Work can be done by applying a force for a certain distance. Based on these definitions, two equations can be written:
- W = ΔE
- W = F * Δx
where W is work, E is energy, F is force, and x is distance. Work is measured in newton-meters (N-m), also known as joules (J).
In class, we lifted and pulled different objects to demonstrate the concepts of work in the real world. The first item we lifted was a backpack.
Using a newton meter, we were able to figure out that the applied force had to be equivalent to 46 N in order to overcome the bag’s force of gravity. We lifted the bag over a distance of 1 meter. Because we know the force applied and the distance, we can use this to calculate the work done:
- W = F * Δx = 46 N * 1 m = 46 N-m = 46 J
This answer also represents the change in energy because W = ΔE. In this case, both the kinetic and potential energy are increasing because it goes from rest to being in motion, and its height (relative to the ground) increases.
Next, we pulled my notebook across a table over a distance of 1 meter.
For this, the force of friction had to be overcome. Once again, we used a newton meter to determine that the applied force, which turned out to be 1.7 N. We can use this to calculate the work:
- W = F * Δx = 1.7 N * 1 m = 1.7 N-m = 1.7 J
This time, only the kinetic energy is increasing because the notebook goes from rest to motion. Potential energy does not change because the height does not change throughout the motion. This also demonstrated that if you apply work, you will become much smarter; I transformed into a THREE-AP STUDENT!
Lastly, to demonstrate a situation in which no work was done, we applied force to an object that would not move.
This made the distance in “F * Δx” equal to zero. Because, anything multiplied by zero is equal to zero, the work done is zero (despite the amazing force):
- W = F * Δx = 4109832785917230895710298375098127 N * 0 m = 0 N-m = 0 J
Another concept that is related to work is power. Power relates to work because it is defined as the rate at which work is done (or energy is dissipated). Using this definition, we can write the equation:
- P = W/t
where P is power, W is work, and t is time. Power is measured in watts (W), which is equivalent to 1 joule (unit of work) over 1 second (unit of time). Another unit for describing power is horsepower (hp), which is approximately 746 watts.
In class, we tried to see if we could produce power that was greater than 1 hp. This was achieved by timing someone (Mr. 3-APs) running up a flight of stairs, determining the amount of work that was required, and then calculating the power to compare with 1 hp.
Data:
- height of stairs: 2.62 meters
- time to climb stairs: 2.34 seconds
- mass of person: 63 kg
The force that must be overcome is the force of gravity:
- Fg = m * g = 63 * 9.8 = 617.4 N
Work is the applied force (equivalent to the force of gravity) multiplied by the distance:
- W = F * Δx = 617.4 * 2.62 = 1617.588 J
Power is the rate at which work is done (W/t):
- P = W/t = 1617.588 / 2.34 = 691.277 W
Ultimately, our runner was not able to generate more than 1 hp because 691.277 W < 746 W = 1 hp.
Through these various activities, we were able to see the real-life applications of the work and power equations. This activity was also important because it connected to some of our previously learned concepts such as forces.
