Physics Honors Impulse and Momentum Study Guide Preview

							                      Physics Honors Impulse and Momentum Study Guide

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Momentum:

1. An object’s linear momentum equals the product of its mass and its velocity.

2. The units for momentum are kilogram∙meters/second (kg∙m/s).

3. Momentum is a vector quantity. The momentum vector points in the same direction as the
velocity vector.

If a 0.14 kg truck is moving to the right and has a velocity of 1.2 m/s, then its momentum is:

                                         p = momentum

                                            m = mass

                                           v = velocity

                                              p = mv

                         p = 0.14 kg x 1.2 m/s = 0.17 kg•m/s to the right

Relationship between momentum and Newton’s second law:

                                           ΣF = ∆P/∆T

                                          ΣF = net force

                                         ∆P = momentum

                                       ∆T = change in time

The change in momentum is called the impulse of the force, and is represented by J. Impulse is
a vector, has the same units as momentum, and points in the same direction as the change in
momentum and as the force:

                                          J = F∆T = ∆P

                                           J = impulse
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Force vs. Time
diagram:




Given the graph above, the force vs. time diagram is shown for a baseball hit by a bat from the
moment of contact to the moment of the baseball leaving the bat. At the moment of contact, the
bat and ball are moving toward each other. The force on the ball increases as they come together
and the ball compresses against the bat. The force then decreases as the ball and the bat lose
contact, and the force is zero again as the ball leaves the bat. Given that:

                 Impulse = change in momentum = average force x elapsed time

We can calculate the impulse by calculating the area under the curve (similar to calculating
displacement by using the area of the velocity vs. time graph); we can do this because the units
for such a calculation are N•S, which is the unit for impulse (change in momentum) according to
the formula:

                                            ΣF = ∆P/∆T,

                                 Which implies that ∆P = ΣF x ∆T

You can also calculate the momentum using the area under the rectangle shown in the graph. The
length of the rectangle is the elapsed time, and the width is the average force exerted on the
baseball. This calculation is valid according to this formula:

                                            J = F∆T = ∆P

Given the above formulas, if a 0.14 kg baseball arrives at 40 m/s and leaves at 49 m/s in the
opposite direction, and the contact time is 5.0 x 10-4 s, the average force exerted on the ball is:
ΣF = ∆P/∆T