Physics 2215: The Ballistic Pendulum

Purpose

Solve a problem by using• Kinematics (Newton’s Laws, Equations of Motion)• Energy/Momentum Conservation.

Use techniques learned in earlier labs:• Measuring techniques• Error calculation• Statistics

Physics 2215: The Ballistic Pendulum

A simple example of kinematic versus energy conservation approaches.

Dropping a ball from a height of 1m. Calculate the velocity justbefore the impact on the floor.

h=1m

vo= 0

vf= ?

y

y = 0

Physics 2215: The Ballistic Pendulum

Kinematic Approach

tgtv )(

2

2

1)( tgty

y

y = 0

s

mg 8.9

htgty ff 2

2

1)(

g

ht f

2

ghg

hgtgtv ff 2

2)(

ghtv f 2)(

Physics 2215: The Ballistic Pendulum

Energy Approach

y

y = 0

ghv f 2

0mghEi

2

2

10 ff mvE

PotentialEnergy

KineticEnergy

mghmvEE fif2

2

1

Physics 2215: The Ballistic Pendulum

Ballistic Pendulum Apparatus

Spring loaded apparatus that “shoots” metal ball.

Pendulum thatcatches the balland is able to swingafter the impact.

Physics 2215: The Ballistic Pendulum

A. Determine the Speed of the Metal Ball Using a Kinematic Approach

Idea: 1) Remove the pendulum part and simply shoot the ball horizontally off the table2) Measure the horizontal and vertical distances from launch to impact on the floor.3) Calculate vo.

vo x

y

Physics 2215: The Ballistic Pendulum

B. Determine the Speed of the Metal Ball Using a Momentum Conservation and Energy Conservation Approach

Idea: 1) Shoot the metal ball into the pendulum so that the metal ball gets stuck in it.2) Measure the maximum angle the pendulum will swing up after the impact.3) Use conservation of angular momentum and conservation of energy to

determine vo.

vo

lmvl

vml

IL

oo

ballballball

2

v

Before impact: After impact:

systemsystemsystem IL

L conserved

Physics 2215: The Ballistic Pendulum

After impact:

v Qmax

At maximum of the swing:

Energy conserved

21 2

1 IE max

2

cos1

cmtot

tot

lgM

hgME

it.in ball with thependulum theof mass of

center theandpoint pivot between distancecml

Physics 2215: The Ballistic Pendulum

Determining the Moment of Inertia of Pendulum with Ball (Isystem)

1) Disconnect the pendulum and reattach it on the other side so that it can swing freely.2) Let the pendulum swing (with the ball in it) and measure the period of oscillation.3) Determine the moment of inertia I using this formula:

cmtot lgM

IT 2

Hint: You can get lcm by balancing the pendulum on the center of mass:

lcm