One Chapter 1

Momentum

Momentum and Motion

• Momentum - the product of mass and velocity.
  • Measures the quantity of motion.

• p = momentum, m = mass, v = velocity.
• Is a vector with direction the same as the velocity
• Units of momentum
  • Mass units times velocity units
  • Most commonly used unit is kgm/s
  • this is a derived unit - a unit that is made up of more fundamental units relating to mass, length, and time.
  • has no specific name.

Impulse and Momentum

• Newton's second law states:

• Where F = force, a = acceleration, and m = mass.
• The force and the acceleration are in the same direction.
• Newton originally stated his law as

• The numerator is change in momentum, the denominator is change in time or time interval and F is force. The change in momentum and the force are in the same direction.
• If we choose our units well, then the proportionality constant will equal 1 and we can write the equation as:

• We can rearrange our force equation relating force to change in momentum to get:

• In this equation, J is impulse.
• Impulse - the product of force and the time the force is applied for.
• The units of impulse are units of force times units of time.
  • The Most commonly used unit is the Newton second (N.s).
• Impulse is a vector in the direction of the net force.
• The equation for impulse given above is used under two conditions.
  1. Force remains constant.
  2. Average force is used if force is not constant.

The Area Under a Force-time Graph is Impulse

• From these calculations, we conclude that the area under a Force-Time graph is impulse.
• When the Force-Time graph is a curved line, we can use calculus to find the area under the line. However, the use of calculus is beyond the scope of this course, therefore we can break the curve into steps and find the arda of each step and total the area.

• The smaller the time intervals are, the closer to the real area this approximation will be.

• Given all this, we can summarize the equations for impulse as:

• Remember that Impulse, Force, momentum and its change, and velocity are all vector quantities.

November 23, 2013