Total Mechanical Energy Lab Report

Some measurements were required for the Conservation of Total Mechanical Energy. The variables used were the thickness of the aluminum block (H), the length of the cart (L), and the distance between the lengths of the cart (D). We registered the mass of the cart (M Cart), as well as the mass of the silver piece (M Silver Piece).

H (m)
0.02552
D (m)
1.023
L (m)
0.1324
M Cart (kg)
0.1718
M Silver Piece (kg)
0.0489
Table 1. Constants part A. This table shows the constants required for the Conservation of Total Mechanical Energy Section.

We divided the first part of the experiment in two sections. For both sections, we measured the average time (T) it took the car to travel the desired distance (d). We calculated the final velocity (Vf ), of
Finally, we measured the length of the cart (L) including the hooks attached to it. These measurements were recorded in the following table:

(M cart ) (kg)
0.1917
(M cart and silver piece ) (kg)
0.3635
(M 3 paper clips ) (kg)
0.003
(M 6 paper clips ) (kg)
0.006
L (m)
0.225
Table 3. Constants part B. This table shows the constants used for the second part of the experiment, The Work Energy Theorem

For this part of the experiment, we measured a new distance (d). We measured the time average (T) of each cart with the corresponding modifications, the time was measured with a photogate. We calculated the final velocity of each cart (Vf ). Afterwards, we calculated the difference of the Kinetic Energies of each cart (KE). Lastly, we calculated the tension in the string that was attached to one of the hooks of the cart (Ft). It is important to mention, that a hanging mass was required to obtain the tension of the string that pulled the cart along the air track; as a matter of fact, the air track was set in level.

d (m)
Trials
t (sec)
T (s)
Vf (m/s)
KE (J)
Ft (N)
W (J)
Cart with 3 paper clips
0.770
It is important to mention, that the cart started from rest; therefore, KE is equal to KEf . With this being said, the KEf of each cart was calculated with equation number one.

Looking at table four, the tension of the string used to pull the cart increased as the mass of the object did as well. In order to calculate the tension of the string, we used the following formula:

(9)

Where m is the mass of the paper clips, M is the mass of cart with the two hooks. The acceleration due to gravity is represented as g (9.80 m/s2). Using this equation and the numbers from table three, we have the following:

(Cart with 3 paper clips)

In this section of the experiment we calculated the work (Wnet ) done by the string of the cart attached, with the following equation:

(4)

Where F is the force (Tension of the string), and d is the distance traveled by the cart. Since the air track was at level, we used for . Therefore, using this equation and the values from table four we have the following:

= 0.0223 J (Cart with no silver piece and 3 paper clips)

For The Work Energy Theorem part, we calculated the percent difference between the KE and the done for each cart.

KE (J) (N)
% Difference
Cart with 3 paper clips
0.0281
0.0223