Newton's Laws:

We have been probing Newton's through our studies of Momentum and Energy Conservation.

Below is a brief summary of Newton's three laws along with momentum and energy conservation. This should be familiar to you.

Kinetic and Potential Energy:

Throwing a ball into the air represents a situation in which the total energy is fixed and there is a continous transformation from kinetic energy to potential energy.

• When the ball is on the ground there and not moving there is no potential energy or kinetic energy
• when the the ball is tossed into the air it will reach a maximum height which is determined by how much kinetic energy it has (air resistance is important however)
• when the ball reaches its maximum height its velocity is 0 and all of the energy in the system is potential energy
• as the ball falls to the ground that potential energy is converted to kinetic energy

Kinetic Energy = Energy Associated with Motion

1/2 mass * Velocity * Velocity = 1/2mv²

Momentum is Mass * Velocity = mv

Conservation of Momentum is a rule of mechanics. your intution has already told you about it.

Consider hitting a baseball. The bat, with some mv, makes impulsive contact with a ball - m_bat is greater than m_ball and since:

(mv)_bat = (mv)_ball

then v_ball is greater than v_bat (provided that you hit the ball and not just air).

Remember that impulse x time = change in momentum.

So an impulsive force (force applied over a small time dt) is a change in momentum:

F * dt = m * dv

where dv = a change in velocity (the force produce an acceleration).

Same principle holds in the situation of cannon recoil:

Potential Energy --> object has a position in a force field

Potential Energy = mass * grav. acceleration * height

PE = mgh

g = gravitational acceleration of the earth

since F = ma and since the earth exerts a continuous gravitational force on all objects of mass, m, then the manifest force is

F = mg this is what weight is !

Now look what Newton says we can now do:

Applications of Conservation of Momentum:

• Elastic Collisions: Collisions that conserve both momentum and energy. Most collisions in the macroscopic world do not do this. In the atomic world, collsions between atoms are often elastic.

• Inelastic Collisions: Collisions that conserve momentum but not energy. The total amount of Energy which is lost, however, is dictated exactly by momentum conservation. That is, the energy which is lost equals that which is required to maintain momentum conservation.

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