Ballistic Pendulum Lab
Joel Cook
Max Zhang
Tian Cih Jiao
Nina Song
Roya Bijanpour
Eric Chong
Kitarou Chen
Lynel Ornedo
Lab performed May 3, 2017
In this lab, we used a ballistic pendulum apparatus to determine the firing speed of a ball from a spring-loaded gun through experimentation and calculation. By measuring the height the pendulum swings, the distance the ball will fire horizontally without the block and the height of the table fired from, we are able to calculate the speed of the ball as it leaves the gun.
Procedure:
The ballistic pendulum apparatus is pictured above. The left side of the apparatus has a spring-loaded gun, a plastic block with a cavity for the ball hangs in the center, and the right side has an arm measuring the angle to which the block swings after the ball inelastically collides with the block. The apparatus was fired from the lowest strength firing position for each trial.
The posts on each corner allow for leveling the base of the apparatus before performing the experiment. Posts are also located on the top of the apparatus for leveling the plastic block. The mass of the ball and the plastic block were measured and recorded, as well.
Five trials were performed in which the angle arm was placed agains the block, the gun was loaded, the area was cleared, and the ball was fired into the block. The angle of the swing was read on the scale provided on the apparatus.
As shown below, after the five trials, the block was removed and the ball was allowed to fire off the edge of the table. A sheet of paper and carbon paper were taped to the floor at the distance the ball would strike the floor. The ball was fired and marked the paper below the carbon paper as it landed. The distance from the end of the muzzle of the gun to the floor where the ball struck was measured and recorded. The height from the muzzle to the floor, as well as the length of the string from the plastic block to the top of the platform, were recorded as well.
Data and Analysis:
Mass of the ball: 0.00759 kilograms
Mass of the block: 0.0789 kilograms
Length of the string: 0.21 meters
Trial #
|
Angle (degrees)
|
1
|
22.5
|
2
|
24.2
|
3
|
27.0
|
4
|
24.0
|
5
|
23.5
|
Average angle: 24.24 degrees
As the diagram above shows, we used the angle Θ and the length of the string, L, to calculate the height of travel of the pendulum, H.
CosΘ = L-H
L
H = L - LcosΘ
H = 21 - 21*cos(24.24)
H= 0.0185 meters
From the height of the pendulum we can calculate the initial speed of the block. Since initial energy is equal to final energy, initial kinetic energy of the block will be equal to the gravitational potential energy of the block at the max height to which it travels:
KEo = GPEf
0.5*Mball*v^2 = M(ball + block)*g*H
v = [2*g*H]^(1/2)
v = [2*9.8*0.0185] ^(1/2)
v = 0.602 m/s
Since the collision of the ball and block is an inelastic collision, the initial momentum is equal to the final momentum:
po = pf
Mball*Vball = M(ball+block)*V(ball+block)
Vball = M(total)*V
Mball
Vball = 0.08649*0.602
0.00759
Vball = 6.86 m/s
We compared this initial speed of the ball to the initial speed from using kinematics and the distance the ball travelled in the second portion.
As the diagram shows, the ball travels horizontally 2.58 meters and vertically 0.99 meters.
y = Vo*t + 0.5*g*t^2
y = 0 + 0.5*g*t^2
t = [2*y/g]^1/2
t = [2*0.99/9.8]^1/2
t = 0.45 s
x = Vo*t
Vo = x/t
Vo = 2.58/0.45
Vo = 5.73 m/s
From kinematics, we calculate the initial speed of the ball as 5.73 m/s
Speed using conservation of energy and momentum: 6.86 m/s
Speed using kinematics and distance travelled: 5.73 m/s
Difference: 16.4 %
Conclusion:
Overall, the lab was successful. The value we calculated from each method was within 17% of each other. There were many sources of error and uncertainty that may have made our results less accurate than they could have been. The apparatus and hanging block may not have been level enough, the method of measuring the angle was not very precise, and it was difficult to get the block to be perfectly still before firing the ball.
No comments:
Post a Comment