Download Ballistic Pendulum - General Physcis - Lab Handouts and more Lecture notes Physics in PDF only on Docsity!
Introductory Mechanics Experimental Laboratory
Ballistic Pendulum
Goals: Observe the relation between kinetic energy and potential energy. Use a data table for interpolation.
APPARATUS A ballistic pendulum is a device consisting of three parts: a spring gun, a ball that can be launched from the gun, and a cup at the end of a pendulum to catch the ball. The spring gun is designed to fire a ball of mass ( m (^) b ) with an initial velocity ( v (^) i ). The pendulum and cup can be moved out of the way. This permits the ball to be fired as a projectile and the initial velocity measured.
When the pendulum is in its lower position, the cup with mass ( m (^) c ) is ready to catch the ball when fired. When the ball is caught in the cup, the energy of the combined cup and ball is used to swing the pendulum up by a height ( h ). A ratchet catches the cup and allows you to read a position measurement by means of a pointer that catches in a groove of the ratchet.
The measurement on the ratchet is marked in units that go from 0 to 40 by 10. There are marks at the halfway points (5, 15, 25, 35), and individual ratchet positions represent steps of 1. The ratchet measure can be converted to height by means of the following table:
TABLE 1. Conversion of ratchet measurement to height.
Ratchet Measurement Height (mm) 0 65 10 73 20 80 30 88 40 96
2 Ballistic Pendulum
To find the conversion for other ratchet measurements requires interpolation. Interpola- tion means estimating the value between two known values. We do this by assuming that the conversion function is a straight line between the two known points. The two points are used to create the equation of a straight line similar to y = mx + b. The actual equation will have offsets because the line is only calculated between two points
For our specific table, we treat the ratchet measurement ( x ) as the independent variable, and the height of the ball ( h ) as the dependent variable. To interpolate look at your mea- surement ( x ). If it’s not in the table, find the measurement in the table ( x 1 ) that is imme- diately below your measurement and its height ( h 1 ) from the table. Find the measurement in the table ( x 2 ) that is immediately above your measurement and its height ( h 2 ). The interpolated height ( h ) for your measurement is
(EQ 1)
THEORY In an earlier laboratory we studied projectile motion. A ball moving horizontally with initial velocity ( v (^) i ) was allowed to fall freely to the ground a distance ( d ) below the launch point. The range (R) beyond the launch point was derived from the kinematics of an object subject only to gravitational acceleration ( g ). The relation between the inve- locity, range, and vertical distance is in EQ 2.
(EQ 2)
Kinetic energy is the energy of motion. It depends on the mass and velocity of an object. When the ball is initially launched it has an initial kinetic energy ( Ki ).
(EQ 3)
When the ball is caught by the cup both the mass and velocity will have changed. The new mass will be the sum of the mass of the ball and the cup ( m (^) b + m (^) c ). The final veloc- ity ( v (^) f ) immediately after the ball is in the cup is given by EQ 4.
(EQ 4)
Using the new mass and the velocity in EQ 4, the kinetic energy after the capture ( K (^) f ) is
(EQ 5)
Potential energy is the energy of position. Objects that are higher can gain kinetic energy as they go lower. This gravitational potential energy ( U ) can be represented as
(EQ 6)
h
x – x 1 x 2 – x 1 = ----------------^ ( h 2 – h 1 ) + h 1
v (^) i R g 2 d = ------
K (^) i^1 2 =--- m (^) b v (^) i^2
v (^) f v (^) i
m (^) b m (^) b + m (^) c = -------------------
K (^) f^1 2
--- (^) ( m (^) b + m (^) c )
m (^) b m (^) b + m (^) c ------------------- ^
2 v (^) i (^2 ) 2
m (^) b^2 v (^) i^2 ( m (^) b + m (^) c ) = =^ ------------------------
U =( m (^) b + m (^) c ) gh
4 Ballistic Pendulum
OBSERVATIONS For each of these questions make a prediction, and support your answer by answering the question “Why?”.
How accurate was the measurement in step 4? What effects might account for the differ- ent positions of the marks?
What parts of the determination of the initial velocity in step 8 were likely to have the greatest error?
How accurate was the measurement in step 10 and 11? What effects might account for the different positions of the ratchet?
Why is kinetic energy not conserved from K (^) i to Kf?
How well was energy conserved from K (^) f to U? If it wasn’t, what factors contributed?
