Lab 15: Ballistic Pendulum

Title: Ballistic Pendulum

Purpose: Determine the firing speed of a ball based on the height to which a target is knocked after an inelastic collision.

Theory: This experiment utilizes conservation of momentum and of energy where momentum of the ball and the target are conserved while the energy of the combined ball and target after collision is conserved as it moves upwards. During the collision, initial momentum of the ball mv is equal to the final momentum of the system (m+M)v. After the collision, the total kinetic energy will be equal to the maximum potential energy of the target and ball where 1/2mv^2 = mgh. Using the ballistic pendulum, angle measurements are taken instead and change in height may be calculated using trigonometric ratios. From this, maximum potential energy may be calculated and equated to maximum kinetic energy. The initial velocity of the ball and target system may then be found and conservation of momentum applied to find the initial velocity of the ball itself.

Apparatus:

• Ballistic pendulum

Procedure:

Pull the ballistic pendulum back to its first locking slot. Adjust the ballistic pendulum as needed to ensure that the ball will accurately strike the target and embed itself. Adjust the ballistic pendulum to position the target directly adjacent to the angle marker at 0 degrees. Fire the gun and record the angle to which the marker was moved. Conduct at least 5 trials. For the second part of the experiment, place the launcher horizontally on a raised flat surface and fire the ball, measuring the height from which it was launched and the distance to which it flew. 

Data and Graphs:

Photo of experimental setup

Table of collected data and calculated values for part 1

Mball	7,6	g
Mtarget	79,7	g
Lstring	20,9	cm
Trial	θ (°)	Δh (m)	Up = KE (J)	v (m/s)	vball (m/s)		Uncertainty
1	17,1	0,009239	0,007913	0,4258	4,891	±	0,2364
2	17	0,009132	0,007821	0,4233	4,862	±	0,2358
3	18	0,010229	0,008760	0,4480	5,146	±	0,2412
4	16,6	0,008711	0,007460	0,4134	4,749	±	0,2337
5	16,5	0,008607	0,007371	0,4109	4,720	±	0,2331
6	16,5	0,008607	0,007371	0,4109	4,720	±	0,2331
				Average:	4,8480	±	0,2356

Table of collected data and calculated values for part 2

hball	0,205	m
	L (m)	Δt (s)	vball (m/s)		Uncertainty
	1,047	0,2044	5,1214	±	0,04892
	1,060	0,2044	5,1850	±	0,04892
	1,062	0,2044	5,1948	±	0,04892
	1,065	0,2044	5,2095	±	0,04892
		Average:	5,1776	±	0,04892

Percentage difference in values of initial velocity

%error

6,366235769

Data Analysis:

The change in height was calculated using Δh = L (1-cosθ), the maximum potential energy was calculating using U = mgΔh and equated to maximum kinetic energy. The velocity of the target with embedded ball was then found using EK = 1/2 mv^2. Conservation of momentum was then applied to find the velocity of the initial ball where mv of the ball equaled (m1+m2)v2 of the combined system.

Conclusion:

The velocity of the ball in part 1 was calculated to be 4.858m/s with an uncertainty of ±0.2356m/s. The velocity of the ball in part 2 was calculated to be 5.178m/s with an uncertainty of ±0.04982m/s.
The difference between these two calculated values is 6.366%. One likely cause for this error is that the two parts of the experiment were conducted during separate days, meaning that a different ballistic pendulum may have been used. Another possibility is that the collision experienced by the ball during the first part of the experiment did not conserve momentum and/or kinetic energy adequately, thus leading to a much lower calculated initial velocity. For this reason, the results of the second part of the experiment are more reliable as fewer energy transfers occur and fewer calculations need to be done to reach an answer.