MOMENTUM

What is Momentum? Momentum is a vector quantity that any moving object with a mass has Momentum has a direct relationship with mass and velocity (the larger the mass or the larger the velocity, the greater the momentum) Formula for Momentum: p = mv p is momentum, m is mass, v is velocity

Quantitative Example Calculate the momentum of a 60 kg person moving at 2 m/s. p = mv p = (60)(2) p = 120 kg·m/s Note: The units for momentum are kgm/s

Conceptual Example A car possesses 20,000 units of momentum. a)What would the car’s new momentum be if the mass doubled? b)What would the car’s new momentum be if the velocity doubled?

Answer Momentum would also double (for either situation) because there is a direct relationship between momentum (p), mass (m), and velocity (v)

A halfback, a tight end, and a lineman are running down the football field. Each player has a mass of 100 kg. Consider their ticker tape patterns below. Which player has the greatest momentum? Which player has the lowest momentum? Explain how you know.

Impulse-Momentum Theorem Impulse-Momentum Theorem To stop an object that has momentum it is necessary to apply a force against its motion for a given amount of time Note: An object with 200 units of momentum is harder to stop than an object with 100 units of momentum, so to stop the first object you may need to apply a greater force for a longer amount of time Impulse = FΔt

Impulse-Momentum Theorem Formula for the theorem: FΔt = Δp = mΔv What does this mean? Impulse (FΔt) is equal to the change in momentum (Δp) which is equal to the mass times the change in velocity (mΔv)

Example Ali has a mass of 50 kg and is driving at 14 m/s in her car when she must suddenly slam on the brakes. From slamming on her brakes her body strikes the airbag, which brings her body to a stop in 0.50 s. What force does the airbag exert on her?

FΔt = Δp = mΔv FΔt = mΔv F = mΔv Δt F = (50)(0-14) (0.50) F = N

Example A hockey player applies an average force of 80 N to a 0.25 kg hockey puck for a time of 0.10 s. Determine the impulse experienced by the puck. Remember, IMPULSE is Force x Change in Time!

Answer Impulse = FΔt Impulse = (80)(0.10) Impulse = 8 N·s The proper units for Impulse are Newton-Seconds (N·s)

Force vs. Time Graph The area under a Force vs. Time graph will give us change in momentum FΔt = Δp (12,000)(.0007) = Δp 8.4 kg·m/s = Δp Remember, the area under a rectangular graph is calculated using base x height!

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