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Who was Isaac Newton? Sir Isaac Newton (1643-1727), an English scientist and mathematician famous for his discovery of the law of gravity, also discovered the three laws of motion. He published them in his book Mathematic Principles of Natural Philosophy in 1687. Today these laws are known as Newton’s Laws of Motion and describe the motion of all objects we experience in our everyday lives.
Newton’s Second Law States: “The acceleration produced by the force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force and is inversely proportional to the mass of the object.” Let’s put this law into simpler terms…
In Other Words… The acceleration of an object is directly proportional to the net force and inversely proportional to its mass. F = m a Force = Mass x Acceleration
What is Force? Force is any push or pull, and they can be balanced or unbalanced. Balanced results in no change in speed or direction, while unbalanced forces result in a change in speed and/or direction.
What is Mass? Mass is the measure of the amount of matter in an object; It is measured in Kilograms.
Is Mass the same as Weight? • No! Weight measures the pull of gravity on an object’s mass. Weight can change according to where the object is. For instance, on the moon, you would weigh 1/6 of what you weigh here on Earth because its force of gravity is much less. • Mass, however, only measures the amount of matter in an object and it never changes!
What is Acceleration? Acceleration is a change in velocity. You can accelerate by: • Speeding up • Positive acceleration • Slowing down • Negative acceleration (Deceleration) • Changing direction
Calculating Acceleration? • To calculate acceleration, subtract the initial velocity from the final velocity, and divide it by the time it took. a = Vf – Vi ____________________________ time
Calculating Acceleration? Barry Boredalot is really bored one day and goes outside to watch ants. He sees an ant carrying a leaf traveling at .1 m/s. The ant, seeing Barry approach, speeds up and runs for safety. In just 2 seconds it accelerates to .6 m/s. Find the ant’s acceleration. V f - V i .6 m/s - .1 m/s .5 m/s .25 m/s2 _____________ = __________________________ = _________________ = Time 2 sec 2 sec
Calculating Acceleration? A semi-truck is stopped at a red light. When the light turns green, the driver pushes on the gas pedal. After 10 seconds, he is moving at 25 m/s. What is his acceleration? V f - V i 25 m/s - 0 m/s 25 m/s 2.5 m/s2 _____________ = __________________________ = _________________ = Time 10 sec 10 sec
What is Acceleration? • Acceleration is DIRECTLY related to the size of the force and the direction of the force. • Acceleration is INVERSELY related to the mass of the object.
In other words…. • Using the same amount of mass… • Large Force = Large Acceleration • Small Force = Small Acceleration • Using the same amount of force… • Large Mass = Small Acceleration • Small Mass = Large Acceleration
Force Causes Acceleration • Acceleration is directly proportional to force. • Example: A golf ball is still until hit by a club. • If you swing the club with a lot of force, the ball will travel farther than if you hit it with a little bit of force.
Mass Resists Acceleration • Acceleration is inversely proportional to mass. • Example: A bus vs. a mouse • The greater the mass the more force it takes to accelerate the object
Force = Mass x Acceleration • The units used for force are Newtons (N) • The units used for mass are kilograms (kg) • The acceleration units are meters per second squared (m/sec2).
Problem Solving • One Newton = the force needed to give a mass of one kilogram an acceleration of one meter per second per second. 1 N = (1kg) (1 m/sec/sec) 1N = 1 kg m/s2
Problem Solving How much force must a 20,000-kg plane develop to achieve an acceleration of 1.5 m/s2 F = m a F = (20,000 kg) (1.5 m/s2) F = 30,000 kg m/s2 F = 30,000 N
Problem Solving If we know two quantities, we can solve for the third: F = m a m = a / F a = F / m
Problem Solving What acceleration is produced by a force of 200 N applied to a 100-kg car? a = F / m a = 200 N/ 100 kg a = 200 kg m/s2 /100 kg a = 2 m/s2
Free Falling Objects • What about acceleration caused by gravity? Do all objects fall at the same rate? • Galileo did his famous experiment off the leaning tower of Pisa. He dropped a 10 kg cannon ball and a 1 kg stone at same time. Both objects landed at the same time, meaning their accelerations were equal…..but why?
Acceleration Due to Gravity • Newton’s second law provides the explanation: • A falling object accelerates toward the Earth because of the gravitational force between the object and the Earth. • The acceleration due to gravity is a constant.
Acceleration Due to Gravity • F/m = a 9.8 N / 1 kg rock = 9.8 m/s2 • F/m = a 98 N / 10 kg cannon ball = 9.8 m/s2 The acceleration due to gravity is a constant on Earth, 9.8 m/s2.
Acceleration Due to Gravity • Why don’t a feather and a bowling ball fall at the same rate if I drop them from a window? Air resistance! • Air resistance is the force of air exerted on a falling object. The air pushes up as gravity pulls down. It is dependent upon the shape and surface area of the object. • In the absence of air resistance, all objects will fall at the same rate due to gravity.
Acceleration Due to Gravity • If you were on the moon an dropped a hammer and a feather at the same time, would they strike the surface of the moon at the same time? YES!
Comprehension Check 1. What acceleration will result when a 15 N net force applied to a 3 kg object? 15 N = 3 kg x 5 m/s2 2. A net force of 1250 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass. 1250 N = 250 kg x 5 m/s/s Click to see answer. Click to see answer.
Comprehension Check 3. How much force is needed to accelerate a 60 kg skier 10 m/sec2? 600 N = 60 kg x 10 m/sec2 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec2? 9800 N = 1000 kg x 9.8 m/sec2 Click to see answer. Click to see answer.
