Ch 8 : Conservation of Linear Momentum

1. Linear momentum and conservation2. Kinetic Energy3. Collision 1 dim inelastic and elastic nut for 2 dim only inellastic4. Collision in CM frame5. Rocket motion (varying mass)

Definition of Linear Momentum and Conservation

To derive the basic result of this chapter Impulse=Dp we integrate the

A. energy equation (W=DK) A time A. Time with respect to:

B. Newton’s 2nd law B. Space

Which of the following is required to get the momentum to be conserved:

A. F net =0 B. F net external =0 C. F net internal=0 D. A or B is ok b/c they are equivalent

Which of the following is true for a system of 2 particles m1 and m2 if the net force on the system is zero?

A. v 1 and v 2 are constant B. m1 v 1 and m2 v 2 are constant C. m1 v 1 +m2 v 2 is constant

As a result of the above we are led to define the momentum of a system of 2 particles m1 and m2 as:

A. p= (m1 v 1 + m2v 2 ) B. p= (m1 + m2 )(v 1 +v 2) C. p= (m1 + m2 )(v Average)

Momentum and Averages

The fact that psystem = pCM is a consequence of :

A. The definition of the CM of a system B. The conservation of momentum C. The internal forces cancelling 2 by 2 D. The equality is not always true

Written in terms of the momentum N2 reads for a system of 2 particles:

A. Fnet= Dp B. Fnet =p1 +p 2 C. Fnet=dp1/dt + dp2/dt D. Fnet=dp1/dt - dp2/dt

To average a quantity Q(x,t) between 2 position A and B which of the following should you compute?

A. B. C. D.

( , )B

A

x

average between A and B xQ Q x t dx ( , )

B

A

t

average between A and B tQ Q x t dt

1( , )

B

A

t

average between A and B tB A

Q Q x t dtt t

1( , )

B

A

x

average between A and B xB A

Q Q x t dxx x

Collisions: General

What is the definition of a perfectly inelastic collision between 2 objects?

A. All speeds remain unchanged B. All final velocities are equalC. The vector sum of the 2 velocities remains unchanged D. Kinetic energy is conserved

During a collision we assume:

A. Internal forces are zero B. External forces are zero C. Both A and B

If initial velocities and masses are known, which of the following can be determined exactly after any collision?

A. All final velocities B. Final velocity of the CM C. Both A and B

What is the definition of a perfectly elastic collision between 2 objects?

A. All speeds remain unchanged B. All final velocities are equalC. The vector sum of the 2 velocities remains unchanged D. Kinetic energy is conserved

Collisions: General

In 2 dimensions the conservation of momentum during a collision gives how many component equations? 1 2 3 4

In addition, if the collision is perfectly inelastic. this assumption give how many more equations in 2 dimensions? 1 2 3 4

For a collision between 2 particles in 2 dimensions, if the masses and initial velocities are known we must solve for the final velocities. How many unknowns do we have to solve for? 1, 2, 3, 4

Or, if the collision is perfectly elastic. this assumption gives how many more equations in 2 dimensions? 1 2 3 4

So in 2 D we have 4 unknowns to solve for: v’ 1x , v’ 1y , v’ 2x , v’ 2y

With momentum conservation we get : 2 equations p1x + p2x = p’1x + p’1x

p1y + p2y = p’1y + p’1y

In addition:

If perfectly inelastic : 2 extra equations: v’ 1x = v’ 2x v’ 1y= v’ 2y ( => solution determined)

If perfectly elastic : only 1 extra equation: K1 + K2 = K’1 + K’2 ( => 1 undetermined parameter e.g angle between the velocities the 2 outgoing particle)

Example space repairExamples: space repair and rr car with grain

Example space repairExample: crash test

Example space repairExample: ballistic pendulum

Example space repairOther examples

Other examples: elastic collision of 2 blocks, inelastic car and truck and CM frame and rocket lift off are studied in the ch8 notes

Ch8 Click. Problems

Ch8 Click. Problems

Ch8 Click. Problems

Ch8 Click. Problems