Lab: May 3, 2017: Ballistic Pendulum

Lab: Ballistic Pendulum 

Amy, John, and Ricardo

May 3,2017

In today's lab we determined the fire speed of a ball from a spring-loaded gun. 

Theory: In this lab a spring-loaded gun fires a metal ball into a nylon block, which is supported by 4 strings. The ball collides inelastically with the block and both the block and the ball rise at an angle, which is measured by the angle indicator on this scale that is marked with half degree markings. By using conservation of momentum we figure the speed of the nylon block and mass of the ball and all this kinetic energy is then turned into potential. At the maximum height achieved by the block and ball, we can say that all the kinetic has now turned into potential and we can derive a formula for the height the block and ball reach.

Begun with momentum, then turned to kinetic, then derived for kinematics

Apparatus and Procedure: For this lab we used the ballistic pendulum provided to us. We had to measure the mass of the ball and zero the needle indicating the angle. We also had to make sure that the block was leveled otherwise the ball would miss the opening of the block and most likely hurt someone. By inserting the metal ball into the loaded-gun, Ricardo managed to pull the by three notches and fired. We did this procedure 5 times and recorded the angle for each collision. We averaged our data and got an angle to plug into our formulas.
We start by recording the mass of the steel ball that we fire and the nylon block that the steel block "sticks" to. The length of the string holding the block is also measured. We level both the ballistic pendulum as well as the strings that hold the nylon block. This way when the ball fires, it gets embedded into the block rather than hitting a side or losing momentum by colliding with the sides before sticking to the block. We then pull back the spring into position (we chose to use three notches in our experiment) and fire the ball. After the collision of the ball onto the block, the two masses travel as one and go up a certain height. We can find the height the total mass goes up by finding the difference between the length of the string at rest and the length times the cosine of the angle. We repeat this experiment 5 times and use the average of the angle.
For the second part of the experiment, we move the nylon block out of the way and tape a piece of paper to the ground where we expect the ball to land. We tape a sheet of carbon paper over this so when the ball impacts the ground it leaves a marking of its position. We fire the ball from our ballistic pendulum three times and take the distance from the ground directly below the point it was fired to the center of the spread of dot markings. We also measure the height from the ground to the point of fire to find the height to use in our kinematic equations.

Data: 

Some measured data before the experimentation:
mass of the ball: 0.0076 kg +/- 0.0001 kg
mass of the block: 0.0795 +/- 0.0001 kg
length of the string (L): 0.195 m +/- 0.001 m

Trial #	Angle (degrees)
1	35.5
2	35.5
3	34
4	34.5
5	36.5
	Average: 35.2

Above is our angle recordings after 5 trials as well as the average.

Measured the distance the launched ball traveled

Using our formula outlined in theory/introduction, the calculated initial velocity of the ball from the first portion of our experiment is 9.581 m/s.

From the second projectile motion part the velocity is calculated to be 7.606 m/s.

For the propagated uncertainty of part 1 the d values for each measurement is:

d variable	d value
Mass of ball	0.00001 kg
Mass total	0.00002 kg
Length L	0.001 m
Angle (radians)	π/360 rad

plugging these values into our propagated uncertainty formula outlined in theory/introduction we get a value of :

Propagated Uncertainty for the velocity of the ball

For this first uncertainty we get 0.5. Which turns out to be an uncertainty of  5% which turns out to be a velocity of about 0.4796 m/s. 

So our propagated uncertainty for the two comes out as:

Conclusion: The main goal of the lab was determining firing speed of the ball from the spring gun using two different methods and comparing the values. We got varied results to the other groups. Our velocity calculated through conservation of momentum and conservation of energy came out to be 9.581 m/s a value higher than the 7.606 m/s calculated from the projectile motion. Looking at the ratios we obtained in our explicit propagated uncertainty calculation, we see that in terms of precision of data, our second setup using projectile motion yielded far more precise results (a 5% uncertainty vs a 0.9% uncertainty).  

There are numerous sources of error within our collision portion of the lab. For starters, the ballistic pendulum we used was rather cheap and inaccurate in many ways. There were a lot of leveling we had to via screws attached to various points on the apparatus and this leveling was done mostly eyeballed. It could be that the ball shot into the block but slightly bounced off the side before being implanted, hence losing energy "before" the collision. Another possibly (probably our main source of error) was our choice to use three notches for our spring load. 

As the ball was shot out into the block the assumption that there was no net force on the system isn't necessarily true. The magnitude of the collision could cause a reaction pull from the tension of the four strings holding the nylon block and that slight pull would be an external force taking momentum away from the system. Another factor is the fact that during the collision the block may not have uniformly ascended and instead wobbled side to side as it traveled up. This may be due to both the strength of the impact as well as cheap equipment. Either way, making the assumption that both momentum and energy is conserved is incorrect and it is backed by the data we calculated. Looking at the different factors that go into the propagated uncertainty calculation, we see that the angle reading uncertainty was a major source of error in our experiment.