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Newton's 2nd law of motion for students

on Jun 25, 2014

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• E.g. In outer space, there is no gravity so everything has zero weight. But, things still have mass. Shaking an object back and forth gives sense of how massive it is because you sense the inertia of it – horizontal changes in motion sense mass, not weight. <br />
• Example – hockey puck in ice <br /> Still until force is placed on it <br /> Stays moving in a straight path until another force causes it to accelerate <br /> Change direction <br /> Speed up <br /> Slow down <br /> Change in velocity  acceleration <br />
• E.g. Kick a soccer ball: what forces acting, causing what motion? <br /> First: accelerates from rest (i.e velocity from 0 to finite) due to your sudden push. <br /> While in air: velocity continues to change - eventually falls to the ground due to the (more gradual) force of gravity. <br />

Newton's 2nd law of motion for studentsPresentation Transcript

• Newton’s Second Law of Motion
• Force and Acceleration • Force is a push or a pull. •Acceleration is when the motion of an object changes. Examples: Speed up Slow down Changes direction •Mass is the amount of matter in an object.
• Mass and Weight • Mass = measure of inertia of object. Quantity of matter in the object. Denote m. • Weight = force upon an object due to gravity: weight = mg Recall: inertia measures resistance to any effort made to change its motion Often weight and mass are used interchangeably in every-day life, but in physics, there is a fundamental difference.
• Mass and Weight • Units: Standard unit for mass is kilogram, kg. • Note mass is an intrinsic property of an object - e.g. it doesn’t depend on where it is, whereas weight does depend on location (e.g. weight is less on moon than on earth…)
• Gravity & Weight • Gravity is the force of attraction that exists between any two objects that have mass. • The force of gravity depends on the mass of the objects and the distance between them.
• Gravity & Weight • Weight is a force, like the push of your hand is a force, and is measured in Newtons. • The force of gravity causes all objects near Earth’s surface to fall with an acceleration of 9.8 m/s². • Your weight on Earth is the gravitational force between you and Earth.
• Moon’s gravity is 1/6 of the Earth’s If you weigh 420 Newtons on earth, what will you weigh on the Moon? 70 Newtons If your mass is 41.5Kg on Earth what is your mass on the Moon?
• Gravity and Weight • How are weight and mass different? • Weight is a force, like the push of your hand is a force, and is measured in newtons. • Mass is the amount of matter in an object, and doesn’t depend on location. • Weight will vary with location, but mass will remain constant.
• • Acceleration = change in velocity time interval • What is the cause of acceleration? – FORCE
• Force causes Acceleration
• (i) Acceleration is created by a net force
• (ii) Mass resists acceleration Acceleration ~ __1_ mass Eg. The same force applied to twice the mass gives half the acceleration Newton’s Second Law Puts (i) and (ii) together: The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. Fneta = m Often stated as Fnet = ma
• Newton’s 2nd Law • Newton’s Second Law states: an object acted upon by an unbalanced force will accelerate in the direction of the force. • If you kick the ball, it starts moving. • The ball accelerates only while your foot is in contact with the ball.
• Acceleration – which way? • Net force action on an object and its resulting acceleration are always in the same direction • The spool demo: – Which way will it roll? – Does it change from top to bottom?
• Force and Acceleration • In this equation, a is the acceleration, m is the mass, and Fnet is the net force. • If both sides of the above equation are multiplied by the mass, the equation can be written this way:
• If you double the mass, you double the force. If you double the acceleration, you double the force. What if you double the mass and the acceleration? (2m)(2a) = 4F Doubling the mass and the acceleration quadruples the force. So . . . what if you decrease the mass by half? How much force would the object have now?
• Mass resists acceleration • Example – Full shopping cart vs. empty shopping cart – The greater the mass the more force it takes to accelerate the object • Acceleration is inversely proportional to mass – Acceleration ~ 1 mass As the denominator increased the whole quantity decreases
• Applications of 2nd Law
• Using consistent units • a = F m • a =acceleration (m/sec^2 ) • F = force (newtons) • m = mass (kg)
• 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 = (1 kg) (1 m/sec/sec) – 1 N = 1 kg m/ sec^2 • If we know two quantities, we can solve for the third
• Newton’s Second Law One rock weighs 5 Newtons. The other rock weighs 0.5 Newtons. How much more force will be required to accelerate the first rock at the same rate as the second rock? Ten times as much
• Newton’s 2nd Law • Newton’s second law of motion can be used to calculate acceleration. • For example, suppose you pull a 10-kg sled so that the net force on the sled is 5 N. • The acceleration can be found as follows:
• Formula Practice A book with a mass of 2.0kg is pushed along a table. If the net force on the book is 1.0N, what is the book’s acceleration? Answer: .5m/s2
• Problem 1 • How much force, or thrust, must a 30,000-kg jet plane develop to achieve an acceleration of 1.5 m/sec^2 • F = ma = (30,000 kg)(1.5 m/sec^2) = 45,000 kg m/sec^2 = 45,000 N
• Problem 2 • What acceleration is produced by a force of 2000 N applied to a 1000-kg car? • a = F/m = 2000 N/ 1000 kg = 2000 kg m/sec^2/1000 kg = 2 m/sec^2 • If the force is 4000 N, the acceleration doubles – 4000N/1000 kg = 4 m/sec^2
• Free Fall explained • Galileo did his famous experiment off the leaning tower of Pisa. – Dropped a 10 kg cannon ball – Dropped a 1 kg stone at same time – Result – accelerations are equal • But why?
• Newton’s law • F = ma • Therefore a = F/m – If an item is large it has a large force and a large mass – If an item is small, it has a small force and a small mass – Either way the RATIOS are the same • F/m = F/m
• Galileo's experiment • a = F/m = 9.8 N/ 1 kg rock = 9.8 m/sec^2 • a = F/m = 98 N/10 kg cannon ball= 9.8 m/sec^2 • Question – 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?
• Answer • Yes. Astronaut David Scott did this exact experiment on the moon. They both accelerated at 1/6 g.
• Newton’s 2nd Law proves that different masses accelerate to the earth at the same rate, but with different forces. • We know that objects with different masses accelerate to the ground at the same rate. • However, because of the 2nd Law we know that they don’t hit the ground with the same force. F = maF = ma 98 N = 10 kg x 9.8 m/s/s98 N = 10 kg x 9.8 m/s/s F = maF = ma 9.8 N = 1 kg x 9.89.8 N = 1 kg x 9.8 m/s/sm/s/s
• Falling and Air resistance • Example – feather and coin in a tube. – With air – coin falls rapidly, the feather flutters down – Without air – both reach the bottom at the same time feather coin weight Air resistance
• Terminal Speed or Velocity • Speed during freefall, when the air resistance on the object equals the weight of the falling object. – Terminal speeds of various objects • Feather – 5 m/sec • Coin – 200 km/hr • Skydiver – 150 – 200 km/h • Parachute – 15-25 km/h
• Eg. Two parachuters, green man heavier than blue man, each with the same size of chute. Let’s ask a series of questions: (1)First ask, if there was no air resistance, who would get to ground first? Both at the same time. (2) They both begin to fall together in the first few moments. For which is the air drag force greater? R depends on area – same for each, and speed – same for each. So initially both experience the same drag force R (3) Who attains terminal velocity first? i.e. who stops accelerating first? When R becomes equal to the weight, then there is zero net force. Since blue’s weight is less, blue attains terminal velocity first. (Note that as they accelerate, R increases, because speed increases but after terminal speed reached, R is const.) (4) Who has larger terminal veloc so who reaches ground first? Green, he reaches his terminal velocity later, after acc. longer, so is faster…
• Circular Motion • A rider on a merry-go-round ride moves in a circle. • This type of motion is called circular motion. • If you are in circular motion, your direction of motion is constantly changing. • This means you are constantly accelerating.
• Circular Motion • If you are constantly accelerating, there must be a force acting on you the entire time. • The force exerted is the centripetal force and always points toward the center of the circle. • In circular motion the centripetal force is always perpendicular to the motion.
• Newton’s Second Law: Note about direction An object accelerates in the direction of the net force acting on it. • Eg. Drop a ball – it accelerates downward, as force of gravity pulls it down • Eg. We considered last time throwing a ball upward. When the ball is thrown upward, what is the direction of its acceleration (after leaving your hand)? Acceleration is downward (gravity) – so the ball slows down as it rises. i.e. when force is opposite to the object’s motion, it will decrease its speed. • When the force is at right-angles to the object’s motion (eg throw ball horizontally), the object is deflected.