Momentum

Momentum and Impulse

Mr. Hawboldt

Open Ended

Which has more momentum: An elephant walking or a fastball thrown by an MLB pitcher. Explain your reasoning

Momentum

• "the impetus gained by a moving object; a product of an objects mass and velocity"

• represented by the letter  $p$  

•  $p=m\times v$  

• has a direction and therefore CAN be negative

• units for momentum are kilograms x meters per second or  $kg\cdot\frac{m}{s}$  

• opposite of less-mentum

Open Ended

Can a pebble have more momentum than a boulder? Explain

 $p=m\times v$  rearranged

•  $m=\frac{p}{v}$  

•  $v=\frac{p}{m}$  

Impulse

• "an impetus that results from a force exerted on an object over time"

•  $J$  represented by the letter

•  $J=F\times t$  

• has a direction therefore CAN be negative

• units for impulse are Newtons x seconds or  $N\cdot s$  

Momentum AND impulse

• momentum is what an object has; you can see it the same way you see velocity

• impulse is what you do; you have to act (apply a force) in order for there to be impulse

Follow the units

• Units for impulse are $N\cdot s$  

•  $N$  are the units for force which come from Newton's Second Law which is  $F_{net_{ }}=m\times a$  

• substituting in the units for each quantity we would see  $N=kg\times\frac{m}{s^2}$  

• replace  $N$  in the units for impulse with  $kg\cdot\frac{m}{s^2}$  and get

•  $\left(kg\cdot\frac{m}{s^2}\right)\cdot s$  

•  $s$  cancels out another  $s$   which gives the final form of  $kg\cdot\frac{m}{s}$  

Impulse can be found by finding the CHANGE in momentum $\left(\Delta p\right)$ 

• in equation form this looks like:  $J=\Delta p$  

• change in momentum is the difference in momenta or $\Delta p=p_f-p_i$  

• combining the last two lines gives:  $J=p_f-p_i$  

• Just like the Work-Energy Theorem, impulse "adds" momentum to a system

Summary

• momentum $\left(p\right)$  depends on mass and velocity and includes direction  

•  $p=m\times v$  

• Impulse  $\left(J\right)$  is an applied force over a period of time

•  $J=F\times t$  

• Impulse can be found by finding the change in momentum

•  $J=\Delta p$  OR $J=p_f-p_i$