3-May-2017: LAB: Ballistic Pendulum

This time, we tried to apply the information we learned to some things about our daily lives. Let's think about when a bullet was fired. It is hard to measure the velocity directly by measuring the distance and the changed of time. However, we can measure them indirectly. For example, we can calculate by the momentum of the system combine by the gun and bullet. In the lab, we picked up two ways to calculate it.

Purpose

Determine the firing speed of a ball from a spring-loaded gun.

Plan

We have two ways to determine the speed of a firing ball.
The first one is to detect it through energy conservative and momentum conservative. We set up an apparatus as following.

When the ball hit the block, we have the function

So as long as we know the speed of the block after the collision, we can know the speed of the ball. 

To calculate the speed of block, we can find how much energy does it have. By the function

We know if we could know the maximum height of the block, then we could find out the energy. 

Therefore, by measuring the angular of the bar, we can get the speed of the ball. Moreover, because it is also hard to measure the height directly, we would measure the angle of bar use the triangle to find the height. 

Another plan is using the most original way, which is fired the ball horizontally.

We can measure the distance it falls down and the distance it goes. To measure how far it goes, we place a piece of carbon under, because it is also hard to Then by the functions

We can calculate the speed easily. 

Set up & data

Experiment 1:

Grab the apparatus that professor has already made for us. 

Measure the mass of the ball and block. 

Level the apparatus including the whole plate and the block. 

Pull back and lock the spring into position, place the ball, and zero the angle. 

Fire the ball and collect the angle. 

Repeat least two steps, until we get enough data. 

Experiment 2:

Then, grab the apparatus on some heights. (We choose on the height of three books, which is 20.5 cm)

Level the apparatus. 

Pull back and lock the spring into position. 

Fire the ball and collect data. (Make sure that the apparatus will not move)

Analyze

(Notice: all the data were converted into international unit before being plugged in)

In the first experiment, 

because the have the functions

We can solve the initial speed is 

Then, plug all the data,

We can get the average speed is 4.88 m/s.

In the second experiment, 

from the functions

We can solve the initial speed is 

Next, plug in the data

And calculate the average is 5.17 m/s

Uncertainty

In the first experiment, we measure 4 different data, and it is acceptable to have some uncertainty. 

By doing some derivative, we can get the uncertainty of the first speed is 

Plug in the data 

In the second one, by doing the derivative we can get

Then, the data tells

Comparing with those data, we can briefly say that the data is fitted within uncertainty, which means the data is good. 

Conclusion

In this lab, we measure the fired ball in two different ways. Except we could make sure how much the initial speed is, we can also compare which way is better for measuring data. 

Moreover, there are some differences between these two data. The first reason will be we actually did experiments in two different days (which might cause a slight change of apparatus). It might also be because the apparatus did not level. We can found out that the beginning data of the first experiment is much closer to the second data (which has less uncertainty). One possible reason is after we fired the ball twice or three times, the apparatus became less leveled. Another reason might be when we measured the distance of the second experiment, we did not measure it parallel with the trajection (which will cause the distance a little bit larger).