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Wize High School Grade 12 Physics Textbook > Linear Momentum and Collisions

Linear Momentum and Impulse

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Linear Momentum and Impulse


Linear Momentum

Linear Momentum (or simply Momentum) is defined as the product of mass and velocity of an object.

Momentum is a vector and measured in kg . m/s.

P⃗=mv⃗\boxed{\vec{P}=m\vec{v}}

If a force is applied to an object, the Second law of Newton could be written in terms of change in momentum as follows:

F⃗=ma⃗         →            F⃗=mΔvΔt\vec{F}=m\vec{a}\ \ \ \ \ \ \ \ \ \rightarrow\ \ \ \ \ \ \ \ \ \ \ \ \vec{F}=m\frac{\Delta v}{\Delta t}

Impulse

Impulse is defined as the change in the momentum of the object if a constant external force of F is applied to the object:


J⃗ =ΔP⃗  =F⃗Δt\boxed{\vec{J}\ =\Delta\vec{P}\ \ =\vec{F}\Delta t}


Wize Concept
If the net external force is zero, the change in momentum is zero and it remains conserved!

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Example: Impulse to a Soccer Ball


A soccer player applies an average force of 180 N during a kick. The kick accelerates a 0.45 kg soccer ball from rest to a speed of 18 m/s. What is the impulse imparted to the ball? What is collision time?

Solution:

We know that impulse is defined as:

J=Δp=pf−pi=FavgΔtJ = \Delta p = p_f-p_i=F_{avg}\Delta t

Since the ball is at rest before the kick, its initial momentum is zero.

pi=0p_i =0

So, we can easily calculate impulse as:

J=pf=mvfJ = p_f = mv_f
J=(0.45)(18)=8.1 kg.m/sJ = (0.45)(18) = 8.1\ kg .m/s

Furthermore, we can find the time duration of the kick again by looking at the definition of impulse:

J=FavgΔtJ = F_{avg} \Delta t

Δt=JFavg\Delta t =\dfrac{J}{F_{avg}}

Δt=8.1180=0.045 sec\Delta t = \dfrac{8.1}{180}= 0.045\ sec


A 2.5 kg Dodge ball hits the back wall of a school gym at 15 m/s at an angle of 50º to the wall. The ball is in contact with the wall for 0.15s before bouncing back at 12 m/s at an angle of 60º to the wall. What average force was exerted by the ball on the wall?