1027

• Run Multiple Choice Generator at h:\shares\physics
• General College Physics:  Run Core Problems by giving the program qzz as your 'course'--enter this when asked for your 3-digit course number.   Do the Physics Quiz 1025.
• University Physics:  Run Multiple Choice Generator for 201 and choose 'Calculus of Uniformly Accelerated Motion'.
• If you miss a problem be sure to click on Comment and explain what you do and do not understand about the question and the given solution.

Text Assignments: 

• General College Physics 6th Edition:  Chapter 7 problems 1, 4, 12, 15, 17, 19, 20, 22, 27, 32, 50

• University Physics and General College Physics 5th Edition:  Problems as assigned in Assignments 19-22, along with reading corresponding text.

How does the momentum change of the steel ball in the collision compare to that of the marble?

Suppose the change in velocity of the ball is -20 cm/s and the change in velocity of the marble is +100 cm/s.

We know that the changes in momentum are equal and opposite.

The change in momentum of the ball is m_ball * `dv_ball and the change in momentum of the marble is m_marble * `dv_marble.  So we know that

• m_ball * `dv_ball = - (m_marble * `dv_marble).

We know, or can easily find from our results, `dv_ball and `dv_marble.

If we know these quantities how do we find the ratio of the masses?

The ratio of the masses is m_ball / m_marble.

To get this ratio:

Starting with the expression

m_ball * `dv_ball = - (m_marble * `dv_marble)

we can divide both sides by `dv_ball to get

m_ball = - (`dv_marble / `dv_ball ) * m_marble

then we divide both sides by m_marble to get

m_ball / m_marble = -`dv_marble / `dv_ball.

In words, the ratio of masses is the negative inverse of the ratio of the velocity changes.

If velocity changes are -20 cm/s and +100 cm/s, then the mass ratio is the negative inverse of the ratio: 

• ratio of masses is -(100 cm/s / (20 cm/s) ) = 5.

Quickly report velocity of ball before and after collision, velocity of marble after collision, and your calculation of the mass ratio m_ball / m_marble = -`dv_marble / `dv_ball.

Experiment from last time:

Rolling a steel ball off a ramp and redirecting its final velocity to the horizontal direction, determine from its projectile behavior how fast it is going as it rolls off the edge.

Then place a large marble on the end of the ramp and let the steel ball collide with the marble.  From the projectile behavior of both determine the velocity of both.

The momentum change of the ball in the collision is equal and opposite to the momentum change of the marble.

From this fact and your data determine the ratio of the ball mass to the marble mass.

Hint:  What is the change in the velocity of the steel ball from just before collision to just after?  What is the change in the velocity of the marble?  How are these answers related to the masses?

University Physics Experiment:

Rolling a steel ball off a ramp and redirecting its final velocity to the horizontal direction, determine from its projectile behavior how fast it is going as it rolls off the edge.

Repeat without redirecting the ball--i.e., the initial velocity of the projectile will be in the same direction as the ramp.

Verify that the undirected ball hits the floor where it should, assuming that its initial speed is the same as when it was redirected.

Determine by projectile behavior the initial speed of the projectile if the ball is rolled down a 60-cm ramp whose rise is the height of the foam cup.

Predict how far the projectile would travel if the velocity was not redirect to horizontal.

Finally predict the ramp slope that would be required for the projectile to hit 3 cm closer to the direct-drop point.