Impulse and Momentum Notes 2/23/15

Chapter 7 These notes cover - Section 7-1, 7-2 and 7-3 (p. 167 – 175)

Conservation of Momentum (Aside) Is a reworking of Newton’s Laws (i.e. Conservation of Momentum is derived from Newton’s Laws)

Momentum Momentum: (vector) is an object or inertia in motion eq. p = m v unit: kg m / s

Momentum and Newton 2 nd Law The rate of change of momentum of an object is equal to the net force applied to it. eq. ΣF net = Δp / Δt (This is how Newton described the 2 nd Law)

Impulse-Momentum Theorem Derived from Newton’s 2 nd Law

Impulse-Momentum Theorem F net t = Δ (m v) impulse = change of momentum

Impulse Impulse: (vector) The time and amount of force acting on an object. eq. J = F net t Unit: N s

Force vs. Time Graph The area under the curve is equal to the impulse

Momentum and Newton’s 3 rd Law  In a collision when objects hit their forces are equal and opposite (Newton’s 3 rd Law) AND their times are equal.  Therefore, their impulses of equal,  AND their change of momenta are equal! (This is the conservation of momentum)

Conservation of Momentum Conservation of Momentum: If there are no non- conservative forces, the total momentum before the collision equals the total momentum after the collision momentum before = momentum after m A v iA + m B v iB = m A v fA + m B v fB (elastic collisions) m A v iA + m B v iB = v fAB (m A + m B ) (inelastic collisions)

Homework Due tomorrow: p. 187 # 1 – 11 (except #4) Due Wednesday: Multiple choice practice exam

Collisions 2/27/15

Types of collisions Completely inelastic – objects stick together, momentum is conserved but KE is not conserved Partially inelastic – object bounce off each other, momentum is conserved but KE is not conserved (Completely) Elastic – objects bounce off each other, momentum is conserved AND KE is conserved

Elastic Collisions Head on collision in 1-D - Conservation of momentum - Conservation of kinetic energy (derivation on page 176) The relative speed of the two objects has the same magnitude, but opposite direction, as before the collision, no matter what the masses are.

Example (#5 from HW) A football player runs at 8 m/s and plows into a 80 kg referee standing on the field causing the referee to fly forward at 5.0 m/s. If this were a perfectly elastic collision, at what would be the velocity and mass of the football player be?

Example A 3.5 kg ball with a velocity of 7.5 m/s in the positive x-direction has a head-on elastic collision with a stationary 9.2 kg ball. What are the velocities of the balls after the collision?

Elastic Collisions – A collision where energy is also conserved. Dropping a ball to the ground and seeing it rebound to the exact same height would be an example of an elastic collision. Of course, this is impossible. Elastic collisions are generally uncommon except on a molecular level such as the interaction of gases in a closed container. p a + p b = p a + p b KE a + KE b = KE a + KE b