CONSERVATION OF MOMENTUM: BALLISTIC
PENDULUM
CATAPANG, JAMIEL S.
2016142388
PHY01 G-223
SCORE
Group Report (40)
Analysis (25)
Conclusion (25)
Presentation (10)
Safe Assign Score (30%
max)
TOTAL
Engr. Ericson D. Dimaunahan
Instructor
October , 2017
ANALYSIS
The experiment all throughout was done really quickly. It was finished for like less
than an hour, approximately 55 minutes or lesser. The preparation of the experiment was
done for almost 10 seconds because it just only needs a pendulum with accessories and a
meterstick. There have been no problems encountered in measuring and setting up of the
experiment. It is just that when we started recording and gathering data, the ball
automatically goes out from the launcher. Also, the ball sometimes do not shoot in the
pendulum bob; hence causing the ball to strike anywhere. We had a hard time getting the
angles and its average for five trials because of those issues.
The design of the experiment, as observed, was particularly manually getting data
needed in the experiment. For example, the mass of the steel ball and the mass of the
pendulum bob were determined not by solving anything. The initial height of the pendulum
bob was also determined through the use of a meterstick. In getting the initial speed of the
steel ball (VI), as observed, the momentum (p) is conserved before and after collision, a
perfect inelastic collision. Thus, it can be calculated from the mass of the pendulum bob with
added mass and the mass of the steel ball.
RESULTS
Table Summary
Mass of the steel ball, m1 = 65.875 g
Mass of the pendulum, m2 = 141.7 g
W/ 100 g added mass = 241.7 g
TRIAL
Angle
1
38°
2
36.5°
3
37°
4
37°
5
36.5°
Average Angle = 37°
Initial height of the pendulum, y1 = 3.2 cm
Derived final height of the pendulum, y2 = 9 cm
Increase in height, y = y2 – y1 = 5.8 cm
HORIZONTAL PROJECTILE
Initial height, y*
3.2 cm
Average horizontal
45.86 cm
distance, x*
Initial speed of the steel
49.7820 cm
ball (Eq. 4), vI
Initial speed of the steel
56.7489 cm
ball (Eq. 7), v1
Percent difference for vI
13.0795%
DISCUSSION
At first, the mass of the steel ball and the mass of the ballistic pendulum were given
to be 65.875-g and 141.7-g with added 100-g mass, respectively. The following needed
materials were set up with the pendulum bob at 0° level. Then, the researchers measured the
initial height (y1) of the pendulum from its base to the reference height, which is the tabletop,
that they had used using a meterstick. The steel ball was then fired to the pendulum with the
same initial height (y1 = 3.2-cm) and noted the corresponding angle for five times. Its average
was calculated, αave = 37°. The vertical distance (y2) was then determined from the base of
the ballistic pendulum to the reference height used by manually setting the pendulum bob to
the average angle computed (α). The increase in height was later calculated by getting the
difference of the initial height (y1) and final height (y2), y = y2 – y1 = 5.8-cm. Since the
researchers have determined the increase height (y), the equation no. 4, V I = (m1 + m2)/m1×
√2𝑔𝑦, was used to determine the first initial firing velocity of the steel ball (EV1).
As for the horizontal projectile, since the experimenters haven’t change the firing
position of the launcher, the firing vertical distance was given to be the same with the initial
height (y1), y* = 3.2-cm. Then, the ball’s distance was predicted before a carbon paper and a
bond paper was used. These papers were used to mark the landing of the ball. The steel ball
was fired and its horizontal distance was measured for five times that averaged x* = 45.86𝑔
cm. Later on, the equation no. 7, V1 = x × √2𝑦∗, was used to compute the second initial speed
of the steel ball to be one of the experimental values (EV2). Lastly, the percent difference
|𝐸𝑉1−𝐸𝑉2|
was calculated with the formula % 𝑑𝑖𝑓𝑓 = 𝐸𝑉1+𝐸𝑉2 × 100, % diff = 13.0795%.
2
SAMPLE COMPUTATION
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑: 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑒𝑒𝑙 𝑏𝑎𝑙𝑙 (𝑉𝐼 ) = ? (𝐸𝑞. 4)
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑒𝑒𝑙 𝑏𝑎𝑙𝑙 (𝑉1 ) = ? (𝐸𝑞. 7)
𝐺𝑖𝑣𝑒𝑛:
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑒𝑒𝑙 𝑏𝑎𝑙𝑙, 𝑚1 = 65.875 g
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑒𝑛𝑑𝑢𝑙𝑢𝑚, 𝑚2 = 141.7 𝑔 (𝑎𝑑𝑑𝑒𝑑 𝑚𝑎𝑠𝑠 = 241.7 𝑔)
𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 ℎ𝑒𝑖𝑔ℎ𝑡 (𝑦) = 5.8 𝑐𝑚
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 (𝑦 ∗) = 3.2 𝑐𝑚
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑥 ∗) = 45.86 𝑐𝑚
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠:
(𝑚1 + 𝑚2 )
𝑉𝐼 =
√2𝑔𝑦
𝑚1
𝑉1 = 𝑥 ∗ √
𝑔
2𝑦 ∗
𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠:
(65.875 + 241.7)
√2(9.8)5.8
65.875
= 4.669070209 (10.66208235)
= 49.782 𝑐𝑚/𝑠
𝑉𝐼 =
𝑉1 = 45.86√
9.8
2(3.2)
= 56.7489 𝑐𝑚/𝑠
𝐴𝑛𝑠𝑤𝑒𝑟𝑠:
𝑉𝐼 = 49.782 𝑐𝑚/𝑠; 𝑉1 = 56.7489 𝑐𝑚/𝑠
CONCLUSION
A ballistic pendulum is an equipment which is applied in measuring the speed of a
ball (or bullet). This apparatus was used for illustrating the principle, Conservation of energy
and momentum. The analysts performed the experiment to observe the principle itself and
determined the initial speed of the steel ball using the ballistic pendulum.
In conclusion, the researchers learned that if there are no external forces acted, the
momentum and energy of the ball and pendulum are both conserved. They can determine and
calculate the initial velocity of the steel ball by the law of conservation of energy and the law
of conservation of momentum. This initial velocity was compared to the data gathered from
the initial velocity of the steel ball in horizontal projectile motion. These data were near to
each other that resulted to a low percent difference; thus, really proves the two principles (or
laws). However, such errors cannot be avoided. These errors are the air resistance coming
from the room and the friction of the system which will enable the system to lose some
energy.