Impulse & Momentum Physics 11.
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Transcript of Impulse & Momentum Physics 11.
Impulse & Momentum
Physics 11
Problem
A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35 m/s. If the batter hits the ball in the opposite direction at 45 m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013s.
Impulse
When an object is accelerated, typically the force will only be applied for a given time
So instead of considering Newton’s Second Law as we have previously discussed it, we will rearrange the equation
Impulse
Use Newton’s Second Law and substitute the definition for acceleration
Rearrange the equation so there are no terms in the denominator
This expression is known as impulse (J)
vmtFJtvmF
amF
Example
A tennis ball is struck by a racquet with a force of 750N; if the time of contact was 0.023s, what impulse was delivered to the ball?
NsJ
sNJ
vmtFJ
17
)023.0(750
Momentum
Momentum can also be defined starting from Newton’s Second Law
The rate of change of momentum can also be used to determine the force
Momentum is defined as the product of an object’s mass and velocity 1st Law of Motion
vmptvmvm
F
tvmF
amF
if
Example
A cyclist is travelling at 32km/h and the bike and rider have a mass of 85kg. What is their momentum?
skgmpsmkgp
vmp
/760)/89.8(85
Impulse-Momentum
Impulse and momentum can be related in order to solve dynamics problems
Substitute the definition for momentum into the impulse equation
ptF
pptF
vmvmtF
vmtF
if
if
Example – again…
A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35 m/s. If the batter hits the ball in the opposite direction at 45 m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013 s.
Example
NFs
smsmkgF
tvmF
ptF
890013.
)/35(/45(145.
Collisions
Physics 11
Conservation of Momentum
The vector quantity momentum will be conserved in any collision That is, the sum of all momenta prior to the
collision will be equal to the sum of all momenta following a collision
Every object that has mass and velocity will have momentum and must be included in the total momentum of the system
Collisions
With any collision, it is imperative that you diagram the system prior to and following the collision and identify all objects involved in the collision
This allows you to ensure that you calculate the total momentum for the system to properly analyze the situation
While this may seem onerous, generally we will be looking at a maximum of two particles
Recall Momentum
Momentum
Impulse
vmp
pvmtFJ
Momentum Conservation Momentum is conserved
This is an expression of Newton’s first law: “An object at rest or in uniform motion will remain at
rest or in uniform motion unless acted on by an external force.”
External forces can change the momentum of a system (Impulse)
FI pp
pvmtFJ
'pp
Momentum Conservation
In interactions between two bodies, momentum of one object can change, but the total momentum of the system remains constant.
'' 2121 pppp
'' 22112211 vmvmvmvm
Types of Momentum Problems Elastic collisions
Inelastic collisions
Explosions
Initial
Initial
Initial Final
Final
Final
Explosions: Recoil
A Barrett M82 is a high calibre sniper rifle. Below are it’s specifications: Barrel length: 73.7 cm Weight: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition weight: 50.0g
Calculate the magnitude force exerted on the riflemen.
Explosion: Recoil
The plan is this Calculate the momentum of the rifle
knowing the momentum of the bullet Calculate the impulse imparted to the
riflemen to stop the gun. Impulse is change in momentum Impulse is force multiplied by time
Need to know the time (how long) the explosion takes.
The Momentum Problem
sm
sm
vkgvkg
vmvmvmvm
vmvmvmvm
05.3')853)(0500.0()')(0.14(
''''0
''
1
1
2211
2211
22112211
Barrel length: 73.7 cm Weapon mass: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition mass: 50.0g
Impulse
tFp
pvmtFJ
We know the person stops the gun, so to find the force, we need to know the interaction time.
Explosions: Recoil Barrel length: 73.7 cm Weapon mass: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition mass: 50.0g
Mm
L
FvIv
smvvdt
tvvd
sm
sm
IF
IF
00173.000.0853)737.0(22
21
Bring it all together
tFp
smkg
sm
IfRifle
p
kgpvmp
ppp
65.42
)'05.3)(0.14(0
1
11 st 00173.0
NxtpF 41046.2
00173.065.42
For Comparison
How many people would have to sit on your shoulder to get the same force?
NxFGun41046.2
NxkgmgFsm
person2109.6)81.9)(70( 2
PersonGun FF
36
Collision
A billiard ball, mass 155g, is travelling at 3.5m/s across the table. It strikes another ball at rest, mass 150g and comes to rest. What is the velocity of the second ball after the collision?