PHYS 2211L - Principles of Physics Laboratory I

PHYS 2211L= - Principles of Physics Laboratory I

Laboratory Advanced Sheet
Ballistic Pendulum

1. Objective. The objective of = this laboratory is to use the ballistic pendulum to predict the initial velocity= of a projectile using the principles of conservation of linear momentum and conservation of total mechanical energy.

2. Theory. The initial velocity= of the projectile will be measured by two independent methods. Those measureme= nts will then be compared.

a. The first measurement method will use the range of a projectile launched horizontally from a given height above the ground to measure the initial velocity of the projectile. From the results of the projectile motion laboratory:

where
v_1i is the initial velocity of the projectile,
g is the acceleration due to gravity near the Earth's surface,
x is the range of the projectile, and
y₀ is the initial height of the projectile above the ground.

b. Derive t= he expression for the initial velocity of a projectile in a ballistic pendulum system (v_1i). Hint: Refer to Serway's discussion of the ballistic pendulum. The pendulum we use will be very simi= lar to that shown Figure 9-11 of your text. Explain all assumptions and show all steps.

3. Apparatus and experimental proce= dures.

a. Equipmen= t.

1) Ballistic pendulum apparatus

2) Meter stick.

3) Carbon paper.

4) Mass balance.

b. Experime= ntal setup. The experimental setup is shown in Figure 1 (provided by the student= ).

c. Capabili= ties. To be provided by the student.

4. Requirements.

a. In the laboratory.

1) Using t= he techniques you learned in the projectile motion laboratory, determine the initial velocity of the launcher by measuring the initial height and range = of the mass when projected horizontally. (Warning: Keep the pendulum portion of the apparatus out of the line of fire during this part of the laboratory.) Conduct five range trials.

2) Measure= the distance from the pivot point to the center of mass of the pendulum/ball system.

2) Conduct= five trials allowing the projectile and the pendulum to collide. Measure the ang= le of the swing for the pendulum/ball system.

3) Measure the masses of the projectile and the pendulum.

b. After the laboratory. The items listed below = will be turned in at the beginning of the next laboratory period. A complete laboratory report is not required for this laboratory.

Para. 2. Theory.

Provide the portion of the theory sect= ion dealing with the development of the equation used to calculate the initial velocity= (v_1i) of the projectile using the ballistic pendulum. Use the following symbols in your development:

1) The dist= ance from the pivot to the center of mass of the pendulum/ball system is R_cm.

2) The angl= e of the swing of the ball and pendulum system is q.

3) The mass= of the ball is m₁; the mass of the pendulum is m₂.

Para. 3. Apparatus and experimental procedures.

1) Provide = a figure of the experimental setup.

2) Provide = a description of the capabilities of the equipment used in the experiment.

Para. 4. Data.

1) Provide = a copy of your data (Annex A contains tables for data).

2) Provide = the following calculations in a spreadsheet (Annex B provides equations for calculations which are contained in the ballistic.xls spreadsheet provided by your instructor):

a) The ini= tial velocity of the projectile as determined by the range method.

b) The unc= ertainty in the velocity of the projectile as determined using the range method.

c) The ini= tial velocity of the projectile as determined using the ballistic pendulum.

d) The unc= ertainty in the velocity of the projectile as determined using the ballistic pendulu= m.

e) The per= cent fractional errors in the initial velocity of the projectile determined using both the range method and the ballistic pendulum.

f) The per= cent discrepancy between the two initial velocities. Use the initial velocity determined using the projectile motion measurements as the accepted value in this calculation.

Para 5.= Results and Conclusions.

1) Provide a statement of the initial velocities determined by each method and their uncertainties.

2) Provide a statement of the percent fractional error and percent discrepancy in your results for the initial velocity determined using the ballistic pendulum.

3) Assess t= he precision and accuracy of the experiment.

4) Describe= sources of random error in the experiment.

5) Describe= sources of systematic error in the experiment.

Annex A
Data

1. Initial height of projectile (use b= ottom of mass).

y₀ (m)	dy<= sub>0 (m)

2. Range of projectile.

trial	x (m)
1
2
3
4
5

3. Mass measurements.

	mass (kg)	dm = (kg)
m₁
m₂

4. Pivot-center of mass distance.

R_cm (m)	dR_cm (m)=

5. Swing angle.

trial	q (= ^o)
1
2
3
4
5

Annex B
Calculations

The calculations associated with the propagation of error are somewhat tedious and are, therefore, computed in a spreadsheet to avoid numerical mistakes. The ExcelTM spreadsheet file is ballistic.xls. Derivations of the formulas used in the spreadsheet are provided.<= /span>

1. The "accepted" initial ve= locity is given by

2. The uncertainty in the "accepted" initial velocity is given by

where,

with= g =3D 9.800 m/s² and dg = =3D 0.005 m/s²,

and<= /p>

3. The calculated value of the initial velocity measured using the ballistic pendulum is given by

4. The uncertainty in the measured ini= tial velocity is given by

where,