IMPULSE , MOMENTUM 2015/2016

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)

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.

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

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

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)

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

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

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

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.

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.

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

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

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

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”.  

Application of Conservation of Momentum

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

More Complicated Collisions

Collisions

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.

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

Viscoelastic materials

deformation

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

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

Effects of Muscle Weakness

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

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

Effects of Muscle Weakness

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

Dynamic Viscosity Shear stress Shear rate

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

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.

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.