pendulum physics

Topics: Energy, Kinetic energy, Plastic shopping bag Pages: 8 (1414 words) Published: October 12, 2013
The Ballistic Pendulum
Crime Lab Physics

You are a criminologist, and have been given a gun which has been used in the commission of a crime. Both prosecution and defense claim that "muzzle velocity" (speed of the bullet as it leaves the gun) is crucial to the case. Your job...FIND IT!

Shown below is a diagram representing a "ballistic pendulum." The bullet is fired into the block, the bullet-block combination rises by a height h as shown, a little physics is applied, and ...voila!...there you have it!

h

Figure 1
Let us proceed: (correct answer choices are given on the next page)

1. The mass of the bullet is 0.01 kg and the mass of the block is 0.99 kg. The bullet is fired into the block and becomes imbedded in it. The bullet-block combination rises by 0.05 meters. What potential energy is stored in the pendulum (bullet-block combination)?

PE = mgh =
a. 50 joules

b. 5 joules

c. 0.5 joules

d. 0.05 joules

2. What was the kinetic energy of the pendulum (bullet-block combination) "immediately" after the bullet became imbedded (i.e. what was the MAXIMUM K.E. of the combination)? KE = PE= (conservation of energy -- no calculation required!) a. 50 joules

b. 5 joules

c. 0.5 joules

d. 0.05 joules

3. What was the velocity of the pendulum (bullet-block combination) "immediately" after the bullet became imbedded (i.e. when its K.E. was maximum)?
KE = 1 mv2
2
a. 0.5 m/sec

v2 = 2KE
m
b. 1.0 m/sec

v=

2KE =
m

c. 1.5 m/sec

d. 2.0 m/s

4. What was the momentum of the pendulum (bullet-block combination) "immediately" after the bullet became imbedded (i.e. when its K.E. was maximum)?
p = mv =
a. 0 kg m/sec

b. 0.25 kg m/sec

Ballistic Pendulum.....5/15/08

c. 0.5 kg m/sec

d. 1.0 kg m/sec

1

Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2008 Exploratorium, www.exploratorium

5. What was the momentum of the block before the bullet hit it? p block = mv = (think about this -- mental calculation -- no calculator required!) = a. 0 kg m/sec

b. 0.25 kg m/sec

c. 0.5 kg m/sec

d. 1.0 kg m/sec

6. What was the momentum of the bullet before it hit the block? p bullet = (conservation of momentum -- no calculation required!) = a. 0 kg m/sec

b. 0.25 kg m/sec

c. 0.5 kg m/sec

d. 1.0 kg m/sec
Answers
1-c; 2-c
3-b; 4-d
5-a; 6-d
7-d

7. What was the velocity of the bullet before it hit the block (i.e. the "muzzle velocity)? p bullet = mv
a. 25 m/sec

v = p bullet =
m
b. 50 m/sec

c. 75 m/sec

d. 100 m/sec

e. 250 m/sec

LAB OR DEMONSTRATION SET-UP & PROCEDURE
Materials
toy dart gun with suction cup darts
balance
1 PVC 1/2 in. pipe, 12 in. long
5 PVC 1/2 in. pipe, 4 in. long
2 PVC 1/2 in. pipe, 2 in. long
3 PVC 1/2 in. 90 degree elbows
2 PVC 1/2 in. T's
plastic water bottle, 500 mL, with top
plastic grocery bag
string
tape, translucent and/or masking
jumbo paper clip
5x8 index card
washer, steel, 3/4 in (approximate mass 50 g)
marker pen
ruler
scissors and/or utility knife
calculator

Assembly
1. Assemble the PVC pieces into the stand shown in Figure 2.

Figure 2

2. Use the utility knife and/or scissors to cut the top end off the water bottle. Make the cut just below where the curvature stops and the straight sides begin. See Figures 3 and 4. 3. Tape the washer to the middle of the bottle. See Figure 3 and 4. 4. Stuff the plastic shopping bag in the bottle in such a way that the bag is pressed out toward the walls of the bottle, forming at least a semblance of an open core down the middle (this isn't too crucial, but you should avoid compressing the entire bag into the bottom of the bottle).

Ballistic Pendulum.....5/15/08

2

Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2008 Exploratorium, www.exploratorium

mark bottle
height

Figure 3

tape paper clip
to bottle...
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