Vertical Displacement Lab Report

Limitations
The angle of release is hard to control, instead of using two ruler that form a 90 degree, a protector should been used
Exact landing spot of the ball on the ground, it’s hard to point out a highly accurate landing spot. Powder should be used, in which it can leave a mark.
The measurement for the vertical displacement, the handmade ball catcher is suspended with light string, as the collision occur, the ball catcher starts to rotate in circular until it reaches the maximum height, this can increase or decrease the measurement of height and make it harder to record the precise measurement for vertical displacement.

Data
Table 1(kinematic experiment). The horizontal displacement of the ball when the mass of the ball, angle of release
and amount of force applied are kept constant
Height of release, dv (cm)±0.05cm Horizontal displacement, x, (cm) ± 0.05cm
Qualitative observation: It’s hard to control the angle of release, the horizontal displacement will be influenced if the angle of release is changed.
Mass of ball catcher, m (g)
± 0.01g Vertical displacement, x , (cm) ± 0.05cm
Table 2 (momentum/ conservation of energy experiment) . The vertical displacement of system when the mass (3.25g) and type of the ball, ball catcher , distant between the ball and the ball catcher, amount of force applied are kept constant . Mass of the ball is 3.25 g.
Qualitative observation : The firmness of the toy gun can results in different speed, also the ball catcher is constantly moving, which can led to error.

Theoretical speed of ball: 3.641m/s

Calculated Data Table
Table 3. The analysis data for determining thr natal velocity and relationship between height of release and the horizontal displacement.
Average horizontal displacement = ( total)/ number of trials
= (52.13cm +50.98cm +51.61cm+54.62cm +53.12cm) /5 = 52.49cm
Error in each average horizontal displacement = ( Range of max and min )/2
=(112.01cm -110.98 cm) /2 = ± 0.52

Average horizontal displacement 2
(52.49cm)2 = 2755.41cm2

Calculation for vi using kinematics: d v = vi t +½ at2 d v = ½ at2 Since there is no velocity before release t=√(2dv/g) Rearrange to solve for t d h=vt substitute t with √(2dv/g) v i =dx √(g/2dv) v i = 0.5249m √(g/(2(0.1115m))) v i =3.4814337836m/s = 3.481m/s

Error in each average initial velocity = ( Range of max and min )/2
=(3.481m/s -3.447m/s)) /2
= ± 0.017

Table 4.The analysis dates for determining the initial velocity and the relationship between mass of ball catcher and vertical displacement.
Mass of the ball catcher, m (g) ±0.01g Mass of the ball catcher -1, m-1 (g-1) Average vertical displacement , dv (cm) Final velocity, vf (m/s) initial velocity Average initial velocity
5.30 0.19 ± 0.00036 8.81 ±0.04 1.32 ± 0.006 3.46 3. 46 ± 0.06
4.13 0.24 ±0.00059 11.86 ±0.05 1.53 ± 0.006 3.46
11.42 0.09 ±0.000077 3.20 ±0.05 0.79 ± 0.012 3.58
8.83 0.11 ±0.00013 4.42 ±0.03 0.93 ±0.006 3.46
6.41 0.16 ±0.00024 6.95 ± 0.06 1.17 ± 0.010 3.47
Average vertical displacement = ( total)/ number of trials
= (8.81cm +8.79cm +8.78cm+8.84cm +8.85cm) /5
= 8.814cm =0.81cm

Calculation for final velocity
E k=Ep
½ mv2= mgh
½ (m1 + m 2 )vf 2=(m1 + m 2 )gh
½vf 2= gh vf =√2gh vf = √(2( 9.81 m/s^2 )(0.08814m)) vf= 1.32m/s
Masses got cancelled in the 4th step of calculating for the final velocity, since both sides has the same magnitude. We can also see that m2 v2i got cancelled in the calculation of initial velocity, since the initial velocity of the ball catcher is zero. Note that for the calculation of average initial velocity, the third velocity is not used, since it’s considered a random error.

Table 5. Percentage error and percentage different between the initial velocity values.
Percentage difference between kinematics and momentum(%) Percentage Error between kinematics and theoretical (%) Percentage Error between momentum and theoretical (%)
0.0515% 0.02473% 0.07628%
Percentage error and percentage difference
%difference =((measured 1-measured 2))/( ((measured 1+measured 2)/2)) *100%
% difference= ((3.461855616-3.46364009))/( ((3.461855616+3.46364009)/2)) *100%
% difference = 0.0515%
Kinematics experiment vs theoretical
%error= l(therotical-experimental )/theroticall *100%
%error = l(3.461-3.461855616 )/3.461l *100%
%error = 0.02473%
Graph
Figure 7. A graphical analysis between height of release and horizontal displacement.

Figure 8. A graphical analysis between mass of ball catcher and vertical displacement.

Through the graphical analysis, we can clearly seen the relationships , thus my hypothesis is proven correct.
Conclusion & Analysis
Inelastic collision and conservation of energy was shown throughout the lab, as momentum and energy are conserved throughout the lab.
My hypothesis regarding to the two experiments are proven correct. As the height of release increases, the horizontal displacement also increase squared, as shown in figure 7. As the mass of the ball catcher increase, the vertical displacement of the system decrease proportionally, as shown in figure 8. The percentage difference between the initial velocity calculated with kinematics and momentum are 0.0515%, which shows the calculation of initial velocity using the two different ways have a relatively similar answer. The percentage error between the theoretical value of initial velocity measured with photo gate and lab quest and the experimental value calculated with kinematics is 0.02473%. The percentage error between the theoretical value of initial velocity measured with photo gate and lab quest and the experimental value calculated with momentum is 0.07628%. Both of the percentage error is relatively small, which prove that the experiment result is valid. The experiment displays the real world context of shooting, in which conservation of momentum and energy and collision are
applied.