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Chapter 9 Force and momentum (9.4 (Elastic collision- when all kinetic…
Chapter 9
Force and momentum
9.1
Momentum
Effect of force depends on mass as well as amount of force
Momentum
is defined as the
product of mass and velocity
Momentum= vector
Sir Isaac Newton- Force needed to change velocity of object
Momentum and Newton's laws of motion
1st Law
Object= at rest or uniform motion unless acted on by force
Force needed to change momentum
If momentum constant
Both velocity and mass constant
One changes and the other changes to resist change in momentum
2nd Law
F=ma- Force is proportional to change in momentum per second
Initial momentum=
mu
Final momentum=
mv
Change in momentum=
mv-mu
F=m(v-u)/t
If m is constant
- Δ(mv)=mΔv so
F=mΔv/Δt=ma
If m changes at constant rate
- Δ(mv)=vΔm so
F=vΔm/Δt
Δm/Δt = change in mass per second
Impulse
- force times the time for which a force acts -
FΔt= Δ(mv)
Force-time graphs
Area under graph= impulse (change in momentum)
9.2
Force-time graph
Area under graph= change in momentum (impulse)
Average force= change of momentum÷ contact time
Rebound impacts
Ball hits wall and rebounds- momentum changes direction
If ball hits wall normally with velocity +u, velocity after= -v so initial momentum= mu and final momentum= -mv
Change in momentum= final- initial
Normal component of initial velocity=
+Ucosθ
Normal component of final velocity=
-Ucosθ
Momentum=
-2mucosθ
9.3
Newton's 3rd law
When two objects interact they exert equal and opposite forces on each other
Forces must be the same type and and acting on different objects to be considered a pair
Conservation of momentum
Object acted on by external force= change in momentum
For a system with interacting objects total momentum before= total momentum after
Testing it
Use two trolleys (known mass). Push Trolley A towards Trolley B so they stick - motion sensor detects and computer records and displays Trolley A's velocity
Measurements show Momentum before= momentum after
Head on collisions
Collision could cause them both to stop- only if initial velocity of objects is equal and opposite (momentum=0)
9.5
When two objects fly apart after being initially at rest, they recoil with equal and opposite momentum
Testing a model explosion
2 trolleys, 1 with a spring-loaded belt and two blocks equal distance from trolleys
V=S/t, t is the same for both as is s
As the have opposite direction, ratio of speed = inverse of the mass ratio so if trolley A travels 2x trolley B mass of A= half mass of B
9.4
Elastic collision
- when all kinetic energy is conserved in the collision
Inelastic collision
- Colliding objects have less kinetic energy than before collision
Objects colliding and sticking together= inelastic, some kinetic energy to surroundings
To calc. work out Ek before and after
