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Momentum & Impulse Topic 2.2
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Momentum What makes an object hard to stop?
Is it harder to stop a bullet, or a truck travelling along the highway? What makes each object hard to stop?
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Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)
Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1) p = mv
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An easy example A truck has a mass of kg and a velocity of 3 m.s-1. What is its momentum? Momentum = Mass x velocity = x 3 = kg.m.s-1.
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Linear Momentum The momentum p of a body of constant mass m moving with velocity v is, by definition mv p = mv It is a vector quantity Its units are kg m s-1 or Ns It is the property of a moving body.
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Conservation of momentum
In a collision between two objects, momentum is conserved (total momentum stays the same) In an isolated system (no outside forces), momentum remains constant isolated system = translational equilibrium We can use this to calculate what happens after a collision (and in fact during an “explosion”). Momentum is not energy!
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Deriving This Law To derive this law we apply Newton´s 2nd law to each body and Newton´s 3rd law to the system i.e. Imagine 2 bodies A and B interacting mass of mA and mB A has a velocity change of uA to vA and B has a velocity change of uB to vB during the time of the interaction t
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Then the force on A given by Newton 2 is
FA = mAvA – mAuA t And the force on B is FB = mBvB – mBuB t But Newton 3 says that these 2 forces are equal in magnitude and opposite in direction
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Therefore mAvA – mAuA = - (mBvB – mBuB) t t mAvA – mAuA = mBuB – mBvB Rearranging gives: mAuA + mBuB = mAvA + mBvB Total Momentum before = Total Momentum after
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Momentum is a vector Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations
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Newton´s Second Law - Revisited
F = ma F = m v - m u t t F = mv – mu F =p t t The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.
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Impulse Where have you heard this term? Some Examples:
I bought that from the internet on impulse after seeing the commercial on TV I got into a fight on impulse after being called a name
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Impulse F = p F = mv – mu t t Ft = mv – mu = p
This quantity Ft is called the impulse of the force on the body It is a vector quantity Its units are kg m s-1or Ns
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Impulse = Change in momentum
Ft = mv – mu = p The quantity Ft is called the impulse, and mv – mu is the change in momentum (v = final velocity and u = initial velocity) Impulse = Change in momentum
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Units or [kg.m.s-2]x[s] = [kg.m.s-1] (mv – mu)
Impulse is measured in N.s (Ft) or [kg.m.s-2]x[s] = [kg.m.s-1] (mv – mu)
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Impulse Note: For a ball (mass m) bouncing off a wall, don’t forget the initial and final velocity are in different directions, so you will have to make one of them negative. In this case mv – mu = 5m – (-3m) = 8m 5 m/s -3 m/s
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Another example A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?
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Another example A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball? 3 m/s -6 m/s
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Another example = 0.3x-6 – 0.3x3 = -2.7kg.m.s-1 Impulse = mv – mu =
A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball? Impulse = mv – mu = = 0.3x-6 – 0.3x3 = -2.7kg.m.s-1 3 m/s -6 m/s
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