Abstract

The experiment performed involved work, power and energy. On the first activity, the time it took for each member to go up and down the stairs was recorded. Afterwards, the work and power done were computed. The most powerful member in the group was student number 2 with power outputs of 239.4 W and 266.0 W when going up and down respectively. On the second activity, the graphs of the potential energy vs. time, kinetic energy vs. time, and mechanical energy vs. time of a ball thrown vertically were all predicted. Finally, the ball was tossed on the motion detector and the graphs of potential, kinetic, and mechanical energies vs. time were all produced using the Logger Pro. Introduction

Work is said to be an act of exerting force. Whatever it is that can make us tired is considered work. The similarity between the conventional meaning and the mathematical meaning of Work is movement. Mathematically, work is defined as W = Fd, where F is the magnitude of the force applied and d is the displacement of the object where force was applied on. Work can be positive or negative; this is due to the positive or negative nature of F and d. When work is positive, this implies that the F and d are of the same sign. This means that the mechanical energy is increased by work in the object. Work is negative when either the value of F or d is negative. This implies that the mechanical energy is lost. Mathematically speaking, Power is the rate at which energy is transmitted. In everyday life, we can explain power through the function of the things around us. The mere action of turning the light on demonstrates power.

The unit for power or P is joule per second (watt) which directly means W done per second. Energy is everywhere, in our bodies and out in the environment. The Conservation of Energy explains that just like heat, energy can neither be created nor destroyed. Instead, energy is transmitted into different types. All kinds of matter contain a lot of energy that they reuse and recycle into the specific type of energy that will enable them to do work. Two of the most widely discussed types of energy are kinetic (KE) and potential (PE) energy, especially in Physics. These types of energy are essential in understanding motion and the universe in general. This study aims to: (1) demonstrate the Law of the Conservation of energy, (2) measure the change in kinetic and potential energies as a ball moves in free fall and (3) determine power output when going up and down the stairs.

Theory

In calculating for Work done by gravity on a person this formula is followed: W(work in Joules)= (force in Newton) (distance in meter) cosΘ, where Θ is the smaller angle between force and distance.

In calculating for the power output this formula is followed: P(power in watt)= W(work in joules)/ t(time in seconds).

Methodology

In this experiment, the materials used were bathroom scale, set of weight, timer. .Activity 1 (power)

The weight of each group member was determined. Each group member was asked to climb up and down the stairs recording its time. The height of the stairs was measured. Using the following data the Work done by each of the member going up and down the stairs was computed along with the power used. Activity 2 (Energy of a tossed ball)

A graph of potential energy versus time of a ball thrown vertically upwards, a graph of a mechanical energy versus the time of the same ball, and a graph of kinetic energy versus time of the same ball was predicted. Given the predicted data the graphs were compared to the actual graph given by using the motion detector to show the actual energy given by the ball being thrown upwards.

Results and Discussion

In Physics, work is an activity that involves force and its movement in the direction of force. Work is dependent on the force of an object as well as on the distance it covers. Among the group members, student 1 has the greatest amount of work because student 1 has the greatest weight. Work, therefore, is directly proportional to the force of an object. The greater the force, the greater work it will be. Power, on the other hand, is commonly defined as the rate of doing work. As seen on table 1, each member has a different amount of power output. The amount of time it took for each member to go up and down the stairs were both measured. Afterwards, the power output was calculated by dividing the work done of each member by the time it took to go up and to go down. When going up the stairs from the second to the third floor, student 1 took the longest amount of time of 17.3s. Note that time is inversely proportional to the power output. The longer time it has, the lesser the amount of power will be yielded. In contrast, the lesser time it has, the greater the power output will be.

However, when going up the stairs, student 4 has the least power output among the group members with 204.4 W and a time of 16.4s. This is because student 4 has lesser amount of work than student 1. Meanwhile, student 1 both has the largest amount of work and longest time making the power output larger. Higher work means higher power. When going down the stairs, student 3 has the least amount of power output. Student 3 has the least amount of work therefore she has the least power among the members. Lesser work means lesser power. Finally, student 2, with a power output of 239.4 W when going up and 266.0 W when going down was the most “powerful” member of the group. It is mainly because of the short time it took for student 2 to go up and down the stairs. Vertical distance between second floor and third floor = __6m__ Table 1.Power outputs of each member.

Member| 1| 2| 3| 4|

Weight (N)| 646.8| 558.6| 539.0| 558.6|

Work in going up (J)| 3880.8| 3351.6| 3234.0| 3351.6|

Time to go up (s)| 17.3| 15.0| 15.2| 16.4|

Power output in going up (W)| 224.3| 239.4| 212.8| 204.4| Work in going down (J)| 3880.8| 3351.6| 3234.0| 3351.6| Time to go down (s)| 15.3| 12.6| 12.8| 12.9|

Power output in going down (W)| 253.6| 266.0| 252.7| 259.8|

On the second activity of the experiment, the graphs were first predicted and then the ball was tossed on the motion detector so that the kinetic, potential and mechanical energies vs. time graphs of the tossed ball will be graphed by the Logger Pro. Figures 1, 2 and 3 present the graphs of the potential energy vs. time, kinetic energy vs. time and mechanical energy vs. time, respectively. Meanwhile, figure 4 is the graph produced of the three energies with respect to time using the Logger Pro. Potential energy has the red line while kinetic energy is shown by the blue line and lastly, black line for the mechanical energy.

Time (s)

PE (J)

Figure 1.Potential energy versus time.

Time (s)

KE (J)

Figure 2.Kinetic energy versus time.

Time (s)

ME (J)

Figure 3.Mechanical energy versus time.

When one member of the group tossed the ball at a height of 50 cm, the ball slows down until it reaches the top of its path and then speeds up on its way back the ground. The moment the ball was tossed, it has its kinetic energy also denoted by KE. As the ball reaches its peak at the height of 50 cm, the potential energy of the tossed ball would be at its greatest thereby losing its kinetic energy. As it goes down and still in its free-fall phase, the gravitational potential energy denoted by PE is again converted back to its kinetic energy. Lastly, if there is no work done by the external non-conservative forces, the total energy will remain constant. This energy is then referred to as the total mechanical energy of an object.

Figure4.Potential energy, kinetic energy and mechanical energy versus time.

Conclusion

Based on the experiment 1, it can be said that work and power are directly proportional in which the greater the work done, the greater the power exerted.

As for experiment 2, it can be concluded the law of conservation of energy indeed applies on the ball being thrown into the air. The kinetic energy of the ball as it was thrown upwards is then transformed into potential energy, whereas the mechanical energy remains constant.

Application

1. The work done when going upstairs and when going downstairs is the same however they do differ in direction. Going upstairs tend to be more difficult than going downstairs because of gravity. In the former, the gravity tends to work against you, pulling you back down while in the latter, gravity works with you.

2. The professor may find the route easier because he/she gets to rest while walking as the gravity while walking along the corridor won’t be won’t be as great as going up the stairs, also walking along a corridor generates no work for the force to hold one’s self upright will be perpendicular to the distance covered. So by taking a break from the stairs, he/she can prepare himself/herself for the next flight of stairs.

3. You should run to the fourth floor in order to not be late because it would be faster and would take lesser time than walking. It can be explained mathematically:

PW=15 watt Distance=12 m

PR=20 watts Weight=750 N

Work done = (12 m)(750 N)

= 9000 J

Power (P) = W/t

tW = 9000 J / 15 watts = 600 s

tR = 9000 J /20 watss = 450 s

Comparing 600 s of walking to 450 s of running, it can be concluded that running is the better option in order to not be late.

4. The change in the potential energy and change in the kinetic energy of an object thrown upward is equal. This is because whatever was “lost” in the potential energy, it will be converted to kinetic energy.

References

Serway, R., & Vuille, C. (2012). Physics Fundamentals 1. Pasig: Cengage Learning.