1. IMPULSE , MOMENTUM
2015/2016

2. DEFINITION OF LINEAR MOMENTUM
In physics, the momentum p of an object is the product of the object’s mass m and velocity v:
Momentum is a vector quantity that points in the same direction as the velocity.
SI Unit of Linear Momentum:
kilogram · meter/second = (kg · m/s)

5. A 1000 kg truck moving at 0.01 m/sec has the same momentum as a 1 kg roller skate moving at 10 m/sec. Both have a momentum of 10 kg m/sec.

6. There are many situations when the
force on an object is not constant.

7. When the collision ocures, the force usually jumps from zero
at the moment of contact to a very large value within
a very short period of time,
and then abruptly returns to zero again

8. DEFINITION OF IMPULSE
The impulse of a force is the product of the average
force and the time interval during which the force acts:
Greek symbol “Delta”
means “the change in…”
Impulse is a vector quantity and has the same direction
as the average force.
SI Unit of Impulse: newton · second = (N · s)

9. IMPULSE-MOMENTUM THEOREM
When a net force acts on an object, the impulse of
this force is equal to the change in the momentum
of the object
IMPULSE
FINAL MOMENTUM
INITIAL MOMENTUM

10. We calculate the injurious effects of collisions from
energy considerations. Similar calculations can be performed using the concept of impulsive force.

13. Impulse and contact time
Knowing the physics helps us understand why hitting a soft object is better than hitting a hard one.

14. Short time contact is the key!
The boxer is moving away when the glove hits, thereby extending the time of contact. This means the force is less than if the boxer had not moved.
The boxer is moving into the glove, thereby lessening the time of contact. This means that the force is greater than if the boxer had not moved.

15. Hitting the bricks with a sharp karate blow very quickly maximizes the force exerted on the bricks and helps to break them.
Increase the force of impact over a short amount of time
and you will deliver devastating damage.

16. AIR BAG
The airbag extends the time over which the impulse is exerted and decreases the force.
The air bag increases the time of the collision

17. Energy and Momentum are CONSERVED quantities.
They always remain constant in a closed system.

18. The Principle of Conservation of Momentum
The total momentum of an isolated system is conserved
In any kind of collision, total initial momentum is equal to total final momentum

19. A 5 kg fish swimming at 1 m/sec swallows a 1 kg fish that is at rest.
A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after “lunch”.
net momentum before = net momentum after
(net mv)before = (net mv)after
(6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vafter)
6 kg.m/sec = (8 kg)(vafter)
vafter = 6 kg.m/sec / 8 kg
vafter = ¾ m/sec
A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after “lunch”.
net momentum before = net momentum after
(net mv)before = (net mv)after
(6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vafter)
6 kg.m/sec = (8 kg)(vafter)
vafter = 6 kg.m/sec / 8 kg
vafter = ¾ m/sec
A 5 kg fish swimming at 1 m/sec swallows
a 1 kg fish that is at rest.
Find the velocity of the fish immediately after “lunch”.
Now the 5 kg fish swimming at 1 m/sec swallows
a 1 kg fish that is swimming towards it at 4 m/sec.
Find the velocity of the fish immediately after “lunch”.

20. Application of Conservation of Momentum

21. BEFORE COLLISION
AFTER COLLISION
Using conservation of momentum, we get
initial momentum of system = final momentum of system

22. More Complicated Collisions

23. Collisions

24. Collisions
Collisions are often classified according to whether the total kinetic energy changes during the collision:
1.Elastic collision—One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision.
2.Inelastic collision—One in which the total kinetic energy of the system is not the same before and after the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

25. Collisions Inelastic collisions
Net momentum before collision = net momentum after collision
Inelastic collisions
- Some kinetic energy lost to heat, etc
Elastic collisions
- No kinetic energy lost to heat, etc

26. Viscoelastic materials

27. deformation

28. Strain Deformation is relative to the size of an object.
The displacement compared to the length is the strain e. L DL

29. Stress A force on a solid acts on an area.
For compression or tension, the normal stress s is the ratio of the force to the cross sectional area. F A

30. Effects of Muscle Weakness

31. Young’s Modulus
A graph of stress versus strain is linear for small stresses.
The slope of stress versus strain is a modulus E that depends on the type of material.
stiff material
Stress s
elastic material
Strain e

32. Material
Young's Modulus Y (N/m2)
Bone
Compression
9.4 × 109
Tension
1.6 × 1010
Brick
1.4 × 1010
Nylon
3.7 × 109
Steel
2.0 × 1011

33. Effects of Muscle Weakness

34. Viscosity
The constant h is the dynamic viscosity and depends on the type of fluid. F vx y

35. Dynamic Viscosity
Shear stress
Shear rate

36. Elastic response is independent of time
The viscous response is generally time- and rate-dependent.

37. Viscoelasticity
Viscoelastic materials exhibit both an elastic response and viscous damping.
Bones, tendons, ligaments, cartilage, muscle, and skin are all viscoelastic.
Viscoelastic materials display both a time dependent and rate dependent response.

38. Mechanical Model
Methods that used to predict the behaviour of visco-elasticity.
They consist of a combination of between elastic behaviour and viscous behaviour.
Two basic elements that been used in this model:
Elastic spring with modulus which follows Hooke’s law
Viscous dashpots with viscosity h which follows Newton’s law.