Newton's First Law: Inertia
When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.
Objects keep moving in a straight line at a constant velocity unless they have a force acting on them. Inertia is the resistance of any physical object to any change in speed or direction.
Newton's Second Law: Force
The vector sum of the external forces F on an object is equal to the mass m of that object multiplied by the acceleration vector of the object.
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Σ = sigma The greek letter Sigma represents a summation of numbers. In this equation it means add up all the forces to get a total force. Sometimes this is called net Force.
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F = force [N, Newtons, kg m/s²] vector
Force is a push or a pull. Force accelerates an object.
m = mass [kg, kilogram]
Mass is a measure of an object's resistance to acceleration.
a = acceleration [m/s²] vector
Example: On a corner kick you use the Magnus Effect curve the ball into the goal. To approximate the magnus effect assume the ball has a net force of 1N towards the goal. How much acceleration does that produce on a 0.43 kg soccerball? How much does the ball deviate from it's original path after 1.5 seconds?
solution
$$F=ma$$ $$\frac{F}{m}=a$$ $$\frac{1}{0.43}=a$$ $$2.33\small\frac{m}{s^{2}}=\normalsize a$$\(a=2.33\), \(\Delta t=1.5\), \(\Delta x=?\), \(v_{i}=0\)
$$\Delta x = v_{i}\Delta t + \small\frac{1}{2}a \Delta t^{2}$$ $$\Delta x = 0(1.5) + \small\frac{1}{2}(2.33) (1.5)^{2}$$ $$\Delta x = 2.62 m$$Example: A 10kg mass is being pulled left with a 2000N force and right with a 1900N force. How will the mass accelerate?
solution
$$\sum F=ma$$ $$-2000+1900=(10)(a)$$ $$-2000+1900=(10)(a)$$ $$-10\small\frac{m}{s^{2}}=\normalsize a$$The mass will accelerate to the left.
Newton's Third Law: Equal and Opposite Forces
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
If you push on an object that object will push back at you.
Example: You push down on the ground with a 1000N force. Describe the magnitude and direction of the force the ground pushes on you.
solution
The force the ground applies is equal and opposite to the force you apply on the ground.
The magnitude is 1000N.
The direction is up.
Example: A boxer's glove applies a 140N force to the face of another boxer. Describe the magnitude of the force the face applies to the glove.
solution
The force is equal and opposite.
The magnitude is 140N.