Foundations of Physics Workshop: The Momentum Collider

The Momentum Collider CPO Science

Key Questions  What is Momentum?  What are some useful properties of momentum?  How can we measure and observe momentum?  What role does momentum play in collisions and how can we use it for calculations?

What is Momentum?  Property of moving matter  Like mass, it measures an object’s resistance to a change in speed or direction  The product of an object’s mass and velocity  IMPORTANT – Remember velocity is a vector so DIRECTION is very important

Setting up the Collider  Allows us to measure and observe momentum  The collider is level and plumb  This ensures the projectile and target will collide squarely  Practice releasing the projectile a few times

Two Objects  Loop the String of the Target over the post on the side of the hanger  Take a few practice swings with the projectile to get a feel for the release

Measure the Projectile’s Velocity  Loop the String of the Target over the post on the side of the hanger  Only the projectile will be swung  Swing the projectile through the photogates once, then catch it so it does not swing back through  Calculate the velocity of the projectile; the diameter of the projectile is 2.50 cm  Velocity is a vector!! It is direction sensitive!

Collect Data  Use the CPO Data Collector and photogates to see how long it takes the marble to break the light beam at points A and B  Calculate speeds

Investigate Motion of Projectile  How would you calculate the velocity?

What about MASS?  Don’t we need MASS to calculate momentum?  We will calculate the mass of the target from our measurements of velocities and the mass of the projectile at the end  How? We will use a “conservative” approach

Conservation of Momentum  Like energy, momentum obeys a conservation law  After the collision both balls may be moving with different speeds and in different directions  the total momentum after the collision must be equal to the total momentum before the collision  m p v 0 = m t v t + m p v p

Different Kinds of Collisions  In an elastic collision, the objects bounce off of each other with no loss in the total kinetic energy.  In an inelastic collision, objects may change shape, stick together, or ‘lose’ some kinetic energy to heat, sound, or friction.  Momentum is conserved in both elastic and inelastic collisions, even when kinetic energy is not conserved.

Two Objects…Again  This time we will use both objects to perform a collision (target diam cm)  Double check to make sure they are aligned  Predict with your group – Elastic or Inelastic?

Performing A Collision  Allows us to measure and observe momentum  The collider is level and plumb  This ensures the projectile and target will collide squarely

Observations  The projectile collided with the target  The projectile actually bounced backward in the opposite direction!  The target swung in the same direction as the projectile, even though the projectile “bounced off” it  Try it again but this time, record data

Calculate the Three Velocities  1 st velocity – the velocity of the projectile as it approaches the collision v o  2 nd velocity– the velocity of the projectile as it bounces back v p  3 rd velocity – the velocity of the target after the collision v t

Does Mass of the Object make a difference?  State your hypothesis  Propose and perform an experiment to test your hypothesis.

Using Conservation of Momentum  the total momentum after the collision must be equal to the total momentum before the collision. Insert velocity values in cm/sec  m p v 0 = m t v t + m p v p

Conservation of Momentum  m p = m t m p  m p = m t m p 32.3  Don’t Forget About Direction!  m p = m t 74.5

m p = m t 74.5  Divide both sides by 74.5  m p 146.2/74.5 = m t  m p 1.96 = m t  If the projectile ball has a mass of 67.2 g, what is the mass of the target ball?

We have used Momentum  We calculated the ratio of the masses involved in the collision  We used the Conservation of Momentum Equation to do it  What would happen if they were the same mass?  What are other ways you can think of to use this equation?