Newton’s Second Law F = ma

Second Law The net force of an object is equal to the product of its mass and acceleration, or F=ma.

Everyone unconsciously knows the Second Law Everyone unconsciously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance than it does lighter objects.

Newton’s Second Law of Motion Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). Who pushed the rock up the hill in mythology?

What does this mean? This also tells us that a larger mass will have a smaller acceleration than a smaller mass if the net forces are equal on both masses. Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force. Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball. Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration.

Doubling the force doubles the acceleration. Doubling the mass but keeping the same force decreases the acceleration So . . . what if you decrease the mass by half? How much force would the object have now? What about doubling the force AND the mass?

Newton’s 2nd Law & Force of Gravity Everyone has heard of the FORCE of gravity We know gravity is a force in nature: Gravity: the force that pulls objects towards each other Since gravity is a force it also obeys Newton’s second law F=ma Since objects fall at the same speed, their acceleration is the same. All objects accelerate at the same rate. Here on Earth the rate is: Ag= 9.8 m/s2 or Ag= 32 ft/s2

F = ma basically states that the force of an object depends on its mass and its acceleration. Something very massive that’s changing speed very slowly, like a glacier, can still have great force. Something very light that’s changing speed very quickly, like a bullet, can still have a great force. Something very small changing speed very slowly will have a very weak force.

Newton’s 3 Laws of Motion Newton’s Second Law of Motion aka F=ma Force = mass x acceleration Can be written as: F=ma ; a= F/m ; m= F/a What is the basic unit for mass in F = ma? Kilogram What is the basic unit for acceleration? Meter/sec/sec Therefore the basic unit for Force is (kilogram)( meter/sec/sec) An object with a mass of 1 kg accelerating at 1 m/s/s has a force of 1 Newton

Second Law (F = ma) How much force is needed to accelerate a 1400 kilogram car 2 meters per second/per second? 1. Write the formula F = m x a 2. Fill in given numbers and units F = 1400 kg x 2 m/sec/sec 3. Solve for the unknown, with units 2800 kg-m/s/s or 2800 N

Force A force is any influence that can cause an object to be accelerated. The pound (lb) is the unit of force in the British system of measurement: 1 lb = 4.45 N or 1 N = 0.225 lb

Newton’s 2nd Law & Weight F=ma Weight is the force of gravity acting on an object’s mass. Therefore weight is a type of Force The formula for weight: Weight = mass x Ag Since Ag= 9.8 m/s2 then Weight = mass x 9.8 m/s2 Remember: 1 newton = 0.22 pounds

Different masses? Newton’s 2nd Law proves that different masses accelerate to the earth at the same rate, but they hit the ground with different forces. 98 N 9.8 N