3.5 Newtons laws of motion and momentum

Newton's first law: an object will remain at rest or continue to travel with constant velocity uless acted upon by a resultant force

Newton's second law: the net force acting on an object is directly proportional to the rate of change of momentum, and is acting in the same direction. 

Newton's third law: when two objects interact, they exert equal and opposite forces on each other. These forces are always of the same type, and have the same magnitude but they act on different objects, and in opposite direction

• The linear momentum,p, of an object is definedd as the product of the object's mass, m, and its velocity 
• p = mv
• the SI unit is kgms^-1
• It is a vector quantity, positive and negative signs show direction

• F = ma is a special case of Newton's second law
• It is true where the mass of the object remains constant during the motion of the object
• It can be derived from Newton's second law:

• The forces acting on a body may vary over time, so we can use impulse to analyse this motion
• It is a measure of change in momentum, so we can use Newton's second law to derive it
• The impulse of a force is defines as the product of the force and the time for which it acts
• 
• Consequently, the area under a force-time graph is equal to the impulse over that time duration, and is also equal to the change in momentum

• When two or more objects collide, there is a transfer of both momentum and kinetic energy
• Providing there are no external forces acting in the system, the total momentum is conserved. This means that the total initial momentum will be equal to the final momentum
• The principle of conservation of momentum states that 'for a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system'
• In a perfectly elastic collision, the total kinetic energy of the system will also remain constant
• However, in an inelastic collision, some of the kinetic energy will be lost to other forms,such as heat and sound energy
• Teh total energy and the momentum are conserved for both collision types

• For a one dimensional collision, the amount of momentum in a direction is always conserved
  • m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
• For this formula to work, one direction of movement must be considered negative
• In two dimensions, the conservation of momentum still applies, however we must consider both the x and y directions separately
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