Step-by-step derivation
In these first steps, we use Newton’s third law followed by his second law.
In the next steps, we apply the definition of the change ǻv in velocity. After some algebraic simplification we obtain the result we want: The
sum of the initial momenta equals the sum of the final momenta.
Step Reason
1. F 1 = –F 2 Newton's third law
2. m 1 a 1 = –m 2 a 2 Newton's second law
3. definition of acceleration
Step Reason
4. definition of change in velocity
5. m 1 vf1 – m 1 vi1 = –m 2 vf2 + m 2 vi2 multiply both sides by ǻt
6. m 1 vi1 + m 2 vi2 = m 1 vf1 + m 2 vf2 rearrange
7.7 - Interactive checkpoint: astronaut
The 55.0 kg astronaut is stationary in
the spaceship’s reference frame. She
wants to move at 0.500 m/s to the
left. She is holding a 4.00 kg bag of
dehydrated astronaut chow. At what
velocity must she throw the bag to
achieve her desired velocity?
(Assume the positive direction is to
the right.)
Answer:vfb= m/s
7.8 - Collisions
Elastic collision: The kinetic energy of the system is unchanged by the
collision.
Inelastic collision: The kinetic energy of the system is changed by the
collision.
In a collision, one moving object briefly strikes another object. During the collision, the forces the objects exert on each other are much greater
Elastic collision
Kinetic energy is conserved