Figure 1.
Light String
Block Pen Mass
Figure 1 shows only how experiment was set up, but Figure 1 does not show the forces that acting on it. First of all, of solving problems with balanced system, should be used and shown the Free Body Diagram.
Figure 2.
0
The Figure 2 includes how the objects acting on the ruler and shows how far they placed from beginning of the ruler. Where is the gravitational force of the block, is the gravitational force of the pen and is the gravitational force of the known mass. Although, all this forces acting to the ruler. (All positions of the objects were measured from the 0cm).
Part B (Experiment 2 explanation)
Experiment 2 of the Object 1 had same set up as the Experiment 1, but the position of objects is different.
Figure 3, which is below, is a Free Body Diagram of the balanced system, where all objects has different placement.
Figure 3.
Where is the gravitational force of the block, is the gravitational force of the pen and is the gravitational force of the known mass. Although, all this forces acting to the ruler. (All positions of the objects were measured from the 0cm)
Part C (Raw data and calculating)
During the Experiment 1 and Experiment 2, were recorded raw data of the placements of the objects. Raw data was recorded into the Table. Table 1, which is below, shows raw data of the placements of the objects during the experiment.
Table 1.
Distance from 0 cm (cm) |
Experiment 1 |
Experiment 2 |
COM of ruler |
48.8 |
48.8 |
Pen ( ) |
73 |
85 |
Block ( ) |
39 |
38.2 |
Known mass ( ) |
93.2 |
95.5 |
The data about the mass of the objects was recorded into the Table 2, which is below.
Table 2.
Mass of the objects (g) |
Experiment 1 |
Experiment 2 |
Known mass |
50 |
50 |
Formulas.
To find the mass of unknown mass, will be used the formula of the momentum (1). Hence, our system is in the equilibrium, can be clearly seen that the sum of the forces is equal to zero. Those means, force that acting to the right side, is equal to the force that acting to the left side. In formula form, it will look like:
In our Experiments that means:
In this formula was used the point of COM of the ruler, because in formula (1) should be used distance between object and COM, but in raw data in the Table 1 said that distance took from 0 cm.
(Therefore, in calculations will not be used the gravitational force of the ruler, because it is fixed in the Centre of Mass).
Calculating for Experiment 1.
For calculation in the Experiment 1, we need substitute raw data from Table 1 and Table to the formula (2).
(3)
Now we need to simplify formula (3):
(4)
In
formula (4) we did not count
,
because we have in both sides so we cancelled it.
Calculating for Experiment 2.
For calculation in the Experiment 1, we need substitute raw data from Table 1 and Table to the formula (2).
(5)
Now we need to simplify formula (5):
(6)
Calculating the unknown masses using the (4) and (6).
To find the unknown values of masses we need to get two simplified formulas from calculating in Experiment 1 and Experiment 2:
Now,
for the easiest way of calculation, need to show
in terms of
=>
Now we need to minus formula (8) from formula (7). We will get:
(9)
Hence the result which was gotten from (9), could be find the first unknown mass of the pen:
=>
=>
=>
=>
=>
So,
mass of the pan was found. Now substitute the value of the
into the formula (7), to find the mass of the second object (block):
=>
The mass of the block was found.
Part D (Calculating and Discuss Errors)
The
original mass of the pen is
and mass of the block is
.
Compare to experimental result, can be clearly seen that was made big error during the Experiments. Hence, errors should be calculated in the percentage.