Momentum and Impulse Unit 4: Momentum, Work and Energy Physics 11

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Momentum:

A car at rest possesses: Amount identified by:

A moving car possesses: and

A moving car also possesses:

Momentum: Symbol: p Product of the objects mass (kg) and velocity (m/s) Is a vector Units = kg·m s p = m v

Example #1: Determine the momentum of a 1.78 kg soccer ball travelling at 4.55 m/s [S] across a soccer field. p = mv = (1.78)(4.55) = 8.10 kg·m [S] s

Car at rest has mass Moving car has mass and velocity velocity = 0

What happens when the car starts from rest and achieves some velocity? The car’s momentum: Increases

What happens when the car moving at some velocity comes to rest? The car’s momentum: Decreases

What causes the increase or decrease in momentum?

Let’s re-examine Newton’s 2nd Law: Already Know: Already Know: Combine: And re-arrange:

Let’s re-examine Newton’s 2nd Law: Then: Change in momentum

Impulse: Symbol: J Product of force (N) and time interval (s) Is a vector Units = N·s J = F Δt

Example #2: A halfback experienced a force of 800. N for 0.90 seconds to the west, what is the impulse? J = F  t = (800)(0.90) = 720 N·s [W]

Momentum and Impulse Connection: To stop such an object, it is necessary to apply a force against its motion for a given period of time Impulse = Change in momentum J = m  v

Momentum and Impulse Connection: Impulse and momentum can be related in order to solve dynamics problems in one step as opposed to two or more Impulse Change in momentum

What causes a change in momentum? How are force and time related? If ThenIfThen

hard to stop, small mass m v m v

hard to stop, small velocity M v

MV

Think about it! A Mack truck has more mass than a roller skate.  Will it always have more momentum than the roller skate? No A Mack truck at rest will have no momentum.

Think about it! Could a Mack truck and a roller skate have the same non- zero momentum. Yes Mack truck moving very slow and roller skate moving very fast.

Example #3: A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35m/s. If the batter hits the ball in the opposite direction at 45m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013s.

Givens: m= 0.145kg, V i = 35m/s, V f = -45m/s, t= 0.013s F=? FΔt = m Δ v F = m (V f – V i ) Δt = (0.145)(-45-35) = N

Summary The impulse experienced by an object is the force x time The momentum change of an object is the mass x velocity change The impulse equals the momentum change

Try it : Page 197 # 29 Page 200 # 30, 31, 32 Page 203 #33, 34, 35 Page 209 # 37-46