Experiment 4 Work Power and Energy

Experiment 4: Work, Power and Energy Laboratory Report Dana Young, Dana Yu, Allen Zafra, Lloyd Pineda* Department of Math and Physics College of Science, University of Santo Tomas Espana, Manila Philippines Pdown= -Wdown/tdown Abstract Where Wup is the work done by gravity Equations for power and work were going up, Wdown, by going down, Fg is the used to determine that power output going weight of the person, h is the vertical distance, upstairs is higher than going downstairs. Kinetic Pup is the power output going up, Pdown, going energy and potential energy are inversely down, tup is the time it took going up, and tdown, proportional in a free falling body. The going down. conservation of mechanical energy states that the total sum of kinetic and potential energy 3. Methodology should be constant, however this experiment has errors involving the total mechanical energy. For activity 1: The vertical height of the 4th floor to the 5th floor of the central laboratory building was 1. Introduction taken by measuring a step using a meter stick Work, power, and energy, are concepts and then multiplying it by the number of total that are present in our world. These concepts are steps, and the weight of each member was taken, related to motion. Knowledge about these and the work going up and down was computed. concepts will help us understand how we can do A timer was used to record the time it took for work more efficiently. each member to go up to the 5th floor from the 4th floor, and back down, and the power going The objectives of this experiment are to up and down were computed. demonstrate the conservation of mechanical energy, to measure change in kinetic and For activity 2: potential energies as a ball moves in free fall, Logger Pro and a sensor was used to and to determine power output when going up graph the kinetic, potential, and mechanical and downstairs. energy of a ball, vertically tossed up. 2. Theory In this experiment, the equations used were equations for work going up and down, and power going up and down. The equations are as follows: Wup= -|Fg|h Wdown= +|Fg|h Pup= -Wup/tup

Figure 2: Graph showing the energy of the ball as it is tossed vertically upward Figure 1: Set-up for graphing the energy of a tossed ball 4. Results and Discussion Table 1 shows the results of the computations for the work done by gravity going up and down, and power output going up and down. Note that the unit for power, W, is watt, not to be confused with the unit for work, W. Student

Wup(J)

Wdown(J)

Pup(W)

Pdown(W)

Young

-2639.88

2639.88

191.02

-190.33

Yu

-3146.22

3146.22

222.82

-223.29

Zafra

-3808.36

3808.36

227.09

-263.16

Pineda

-2380.22

2380.22

141.93

-164.61

Table 1: Work going up and down, and power going up and down The work going up has negative values because the force of gravity is opposing the force exerted going up the stairs. This means it requires more work to go up the stairs than down. The values for power going up is larger than the values for power going down, so it takes more power to go up the stairs than down, this is in conjunction with the fact that it takes more work to go up than down.

Figure 2 shows the graph of energy versus time, recorded by the Logger Pro as the ball was tossed vertically upward above it. The red line shows the values for potential energy, the blue line shows the values for kinetic energy, and the black line shows the values for the total mechanical energy. The part of the graph that is in between 0.2s and 0.3s is the part that most accurately shows the energy levels of the ball. It shows us that as kinetic energy goes up, potential energy goes down, and vice versa. Meanwhile, the total energy is the sum of these two energies. The total mechanical energy of this object should be constant, as dictated by the conservation of mechanical energy that states the the total kinetic and potential energy must be constant, but the graph does not appear to show a constant value of total energy. This is likely because the ball was not tossed perfectly for the sensor to read optimum results. 5. Conclusion Work and power equations were used to determine the power output of going up and down stairs. The results indicate that the power output going upstairs is higher than going downstairs, due to the force of gravity acting on the person climbing, therefore it is harder to go upstairs than downstairs.

Kinetic energy of a free falling object is inversely proportional to its potential energy. The conservation of mechanical energy was not demonstrated very well in the results, possibly due to errors in tossing the ball. 6. Applications 1. The work done going up has a negative value because the force of gravity is in opposition to the person’s force that is going up. It is more difficult to go upstairs than downstairs because as you go upstairs, the force of gravity, which is pulling you down, is opposing your force, which is going up. When going downstairs, the direction of your motion is the same as the direction of gravity, so it is easier.

b.) t=Fd/Pr t=(750N)(12m)/(20 J/s) t=450s

∴ If I have 5 minutes or 300s before my class, I will be late whether I run or walk. However, running will get me to my class in less time than walking, so running would be the better choice. 4. As the potential energy of the ball changes, its kinetic energy also changes. As the potential energy decreases the kinetic energy increases. Thus, it can be said that the ball’s potential energy is inversely proportional to its kinetic energy as it is thrown vertically up.

2. The work the professor does during his movements towards the third floor is the same because his displacement is the same. However, the power exerted by the professor is not the same because the time it takes to get there is different. It is less exhausting for him to get to the third floor by walking along a corridor before ascending up another set of stairs again because it the work was distributed along a longer period of time, making it feel like less energy was expended for his displacement. 3. Given: P for running=Pr=20 J/s P for walking=Pw=15 J/s d= 12 m F= 750 N t= Fd/P (derived from P= W/t) a.) t=Fd/Pw t=(750N)(12m)/(15 J/s) t= 600s

7. References Cutnell, J.D., & Johnson, K.W. (2015). Introduction to Physics and WilePlus Set. New Jersey, NJ: John Wiley & Sons, Inc. http://physics.bu.edu/~duffy/py105/EnergyCons ervation.html