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Unit 4: Momentum, Work and Energy Momentum and Impulse Physics 11 Back to bad humour… Momentum: A car at rest possesses: Inertia Amount identified by: mass (m) A moving car possesses: Inertia and velocity (v) A moving car also possesses: momentum ( p ) p mv Momentum: • Symbol: p p=mv • Product of the objects mass (kg) and velocity (m/s) • Is a vector • Units = kg·m s 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 velocity = 0 p mv p0 Moving car has mass and velocity p mv p mv 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? Force Let’s re-examine Newton’s 2nd Law: Already F ma Know: Combine: v F m t v Already a t Know: And re-arrange: Ft mv Let’s re-examine Newton’s 2nd Law: Ft mv Then: Ft Impulse (I) mv Change in ? momentum Impulse: • Symbol: J J = F Δt • Product of force (N) and time interval (s) • Is a vector • Units = N·s Example #2: • A halfback experienced a force of 800. N for 0.90 seconds to the west, what is the impulse? J =Ft = (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 J=mv 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 Ft mv Ft mv f mvi Ft p f pi Ft p Change in momentum Ft (mv ) What causes a change in momentum? Force How are force and time related? If t Then F If t Then F hard to stop, small mass m v hard to stop, small velocity Mv 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 nonzero 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, Vi= 35m/s, Vf= -45m/s, t= 0.013s F=? FΔt = m Δ v F = m (Vf – Vi) Δt = (0.145)(-45-35) 0.013 = - 890 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