Lab Report: Conservation of Mechanical Energy Theory (Term Paper Sample)

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Lab Report: Conservation of Mechanical Energy
Abstract
In this laboratory experiment, a system of pulley with a string, an air track attached to a cart, and a weight hanger were used in a tandem with various masses to model an experiment to establish the law of conservation of energy. The lab was conducted in two parts. The first part varied the weights on the mass hanger while the second part changed the cart's weight by adding small weights step by step in it. The relative percentage error was calculated for each part. For the first part, the value of the relative percentage error was found to be ranging between 0.003 percent to 0.291percent. For the second part, the percentage relative error was found to range between 0.0358 percent and 0.0876 percent.
Introduction and Theory
Energy is defined as the ability to do work. Basically, it is a product of force and distance (Dukert 5). Force is defined as a pull or push on an object resulting into the object interacting with other objects around it (Goswami and Kreith 11). Whenever any two objects interact, there is a force between them. When the interaction stops, the two bodies cease to experience the force. A force acting on a body has several impacts. A force can induce motion in a body at rest, increase the speed of a moving body, stops a moving a body, or deforms a body. When a force acts upon an object, it does work. The work done is given by equation 1.
W=F x S----------------------------------------------------------------------------------------------------- (1)
Where W is the work done by the force, F is the magnitude of the force, and s is the object's displacement. The body gained an energy whose magnitude is equal to the work done on it. The energy gained is known as mechanical energy. There are two distinct types of mechanical energy. These are kinetic and potential energy. Kinetic energy is the type of energy that is possessed by a moving body. The kinetic energy can be calculated by equation 2.
K.E = 12 mv2------------------------------------------------------------------------------------------------- (2)
Where K.E is the magnitude of the kinetic energy, m is the mass of the body, and v is the velocity at which the body moves. On the other hand, potential energy is defined as the type of energy possessed by a body at rest (Viegas 26). The value of potential energy varies with the place’s gravitational field strength and the position of the body with respect to the ground. Potential energy is given by equation 3 shown below.
P.E = mhg --------------------------------------------------------------------------------------------------- (3)
Where P. E is the potential energy, m the body’s mass, h is the distance from the ground to the point where the body is, and g is the gravitational field strength of the place.
The law of conservation of energy states that energy can neither be created nor destroyed, but can only be converted. Therefore, for mechanical energy, the sum of kinetic and potential energy at any given point is constant. This is shown by equation 4.
E= K.E +P.E = C ------------------------------------------------------------------------------------------- (4)
Where E is the total sum of mechanical energy; C is a constant, and K.E is kinetic energy and P.E is potential energy.
In this lab, various pieces of equipment were used to model and experiment to establish the validity of the law of conservation of energy. The initial sum of mechanical energy is determined from equation 5 shown below.
E0 = (K. E) 0 + (P.E) 0 -------------------------------------------------------------------------------------- (5)
Where E0 is the sum of the initial mechanical energy, and (K. E) 0 and (P.E) 0 are the initial kinetic energy and potential energy respectively. The theoretical relative percentage error was determined from equation 6 shown below.
Relative Percentage Error = ΔEE0 x 100 ------------------------------------------------------------------- (6)
Where E0 is the initial mechanical energy and ΔE is the change in mechanical energy.
Objective
The main objective of this laboratory experiment was verify the validity of the law of conservation of energy.
Procedure
The secondary and primary gates, air cart, air track, string, mass hanger, and a pulley system were obtained and put in place. The air track was placed on one of the tables and the pulley on the other table. The air track was then leveled on the table. Next, the cart was placed on the air track. After this, the primary gate such was set such that it was right after the screw on the air cart. A piece of string was then properly tied on the screw on the air cart. Next, the string was tied onto to the mass hanger and taken over the pulley system. The distance from the bottom of the mass hanger to the ground was then measured keenly and the value recorded. The value was recorded as s. After obtaining the value of the displacement, the secondary gate was placed exactly 51.4 cm away from the primary gate.
When the assembly was completely set, the mass on the mass hanger was varied and the value of each mass recorded as m. The values were measured in grams and in steps of 5, 25, 50, 75, 100, 125, 150, 175, 200, and 250. The distance, s, between the bottom of the mass hanger and the ground and the mass of the cart were kept constant. The table below shows the independent variable and dependent variables for the experiment 1.

Mass of Hanger (m) in grams

Mass of Cart (M) in grams

Distance (S) in cm

Set 1

5

215.72

51.4

Set 2

25

215.72

51.4

Table 1: Independent variable and independent variables for experiment 1.
The air track and the photogates were then turned on. Next, the time taken by the cart to move from the primary gate to the secondary gate was recorded. Each experiment was carried out in several sets and each set carried out in trials and the values for each trial recorded. After conducting each set, the masses were adjusted accordingly. The same procedures were followed for the experiment 2, except for the independent variable. For experiment 2, the mass of the cart was varied by adding masses to it. The masses added were in steps of 25, 50, 75, 100, 125, 150, 175, 200, 225, and 250 g. The total mass was then calculated by adding the added mass to the mass of the cart. The time taken by the cart to move from the primary gate to the secondary gate was recorded according. The table below shows the independent variable dependent variables for experiment 2.

Mass of Cart (M) in grams

Mass of Hanger (m) in grams

Distance (S) in cm

Set 1

240.72

50

30.1

Set 2

265.72

50

30.1

Table 2: Independent variable and independent variables for experiment 2.
Data
The results for the experiments are as shown below
Experiment 1 data
.
Table 3: Experiment 1 data
Table 4: Experiment 2 data
Results
The data was processed in the Microsoft Excel program as shown in the appendix section, and the results are as shown in the tables below.
Table 5: Results for experiment 1
Table 6: Results for experiment 2
Discussion and Conclusion
The law of conservation of mechanical energy states that energy can neither be created nor destroyed. The law means that at any given point, the total ...