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Newton’s Second Law of Motion Force & Acceleration

Newton’s Second Law of Motion Force & Acceleration. Chapter 3. Galileo Takes It a Step Further…. Galileo’s experiments showed that objects fell regardless of their mass Further experiments showed that objects increased their velocities by a given amount each second…They went faster and faster

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Newton’s Second Law of Motion Force & Acceleration

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  1. Newton’s Second Law of MotionForce & Acceleration Chapter 3 Presented by April Senger

  2. Galileo Takes It a Step Further… • Galileo’s experiments showed that objects fell regardless of their mass • Further experiments showed that objects increased their velocities by a given amount each second…They went faster and faster • The rate of change of velocity is called acceleration Presented by April Senger

  3. What is the other name for the gas pedal in your car? The brake is the negative acceleration of deceleration Velocity is change in speed or direction The steering wheel can also accelerate your car even if the speed stays constant Acceleration is the change in velocity divided by the time interval in which it occurred a = ∆v/t ∆ means change in Acceleration Presented by April Senger

  4. Acceleration Example • If I am traveling 50 mi/hr and increase my speed to 55 mi/hr in one second what is my acceleration? • a = 5 mi/hr = 5 mi/hr/s or 5 mi/hr·s 1 second • If it was an increase over an hour? • a = 5 mi/hr = 5 mi/hr2 1 hr • Did anyone remember to write a direction? Presented by April Senger

  5. More Acceleration Examples • If an object is falling and increases its speed 10 m/s every second, what is its acceleration? • a = 10 m/s = 10 m/s2 Downward 1 s • This is known as free fall and will always have a value of 9.8 m/s2 or about 10 m/s2 • If you throw an object up, it slows at the same rate Presented by April Senger

  6. Still Have the Force? • Remember that net force is the combination of all the forces acting on an object • The object will always move in the direction of the greatest force • If you double the force it doubles the acceleration • Tripling the force, triples the acceleration • We can state the force is directly proportional to the acceleration (the change the same) • Acceleration ~ net force • ~ means directly proportional to Presented by April Senger

  7. Concept Check • If you push on a shopping cart it will accelerate. If you apply four times the net force, how much greater will the acceleration be? • If the net force acting on a sports car is increased by five, how much greater will the acceleration be? Presented by April Senger

  8. What Next? • Forces produce acceleration • The amount of acceleration is dependent on something else… • It depends on the mass of the object being pushed or pulled Presented by April Senger

  9. Mass • Mass is a measure of how much material an object contains • Objects can have a high density which means that there are many atoms in a certain area than something that isn’t dense • Mass and inertia correspond Presented by April Senger

  10. How? • If you kick an empty can, it accelerates with little force • If you kick a can of rocks, it requires more force and has a greater resistance to move • More massive objects have greater inertia than lighter objects • Basically, they more resistant to changing their current motion Presented by April Senger

  11. Where Might You See This? • Most people use an object’s inertia without thinking about it • If you are driving a truck that is fully loaded, you will need a bigger engine to move the mass at your desired velocity • You will also need better brakes to decelerate • Auto designers, farmers, and even students driving to college use these concepts every day Presented by April Senger

  12. Volume • Volume is a measure of space • Mass is measured in kilograms • Volume is measured in cubic meters • What has a greater mass, a pound of feathers or a pound of lead? • What has greater volume? Presented by April Senger

  13. Wait! I Mean Weight… • Mass is the amount of matter in the object • Weight is the force due to gravity that acts on an object’s mass • If you went to the moon, would you mass change? • Would your weight change? Presented by April Senger

  14. Lazy Bones • Mass is sometimes called a measure of inertia or “laziness” of an object to change its state of motion • Shaking an object back and forth gives you a good idea of an object’s inertia • Mass and Weight are proportional to each other • What does this mean? Presented by April Senger

  15. Extra Credit • When you go to bed find a place to reach as high as you can and mark it • When you wake up, see if you can beat the mark you made last night • Gravity compresses you spine over the course of the day. You should gain 2-3 cm overnight • Have your parents write me a short note about your experiment and have it in by tomorrow Presented by April Senger

  16. Concept Check? • Does a 2 kg iron block have twice as much inertia as a 1 kg iron block? Twice as much mass? Twice as much volume? Twice as much weight when weighed at the same location? • Does a 2 kg iron block have twice as much inertia as a 1 kg bunch of bananas? Twice as much mass? Twice as much weight when weighed at the same location? • How does the mass of a bar of gold vary with location? Presented by April Senger

  17. Kilograms to Newtons • The standard unit of measurement is the kilogram or kg • The standard unit of force is a Newton or N • A 1 kg bag weighs 1 N • This is weight and not the amount of matter • Away from the Earth, the 1 kg bag would weigh differently and the matter would stay the same Presented by April Senger

  18. More Conversions • For simplicity, 9.8 N will be rounded to 10 N • If you know the kg multiply it by 10 to convert to newtons • If you have newtons divide by 10 to convert to kg • 1 kg is equal to 2.2 pounds on Earth’s surface • 1 lb is equal to 4.45 N on Earth’s surface Presented by April Senger

  19. Concept Check • Why is it okay to say a 1 kg bag of sand weight 10 N, but a 1 kg bag of gold weighs 9.8 N? Don’t they weigh the same? • Think about when we need to be accurate and when it is okay to round Presented by April Senger

  20. Acceleration and Mass • Acceleration and Mass are inversely proportional • a ~ 1/mass • Inversely means that the two values change in opposite ways • For instance, increasing the mass by 3 means that the acceleration result in 1/3 as much • If the mass is decreased by ½ then the acceleration will increase by 2 • One increases and the other decreases Presented by April Senger

  21. Concept Check • Suppose you’re offered either ¼ of an apple pie or 1/8 of the pie. Which piece is larger? • Suppose you apply the same amount of force to two carts, one cart with a mass of 4 kg and the other with a mass of 8 kg. • Which cart will accelerate more? • How much greater will the acceleration be? Presented by April Senger

  22. Although Galileo introduced inertia and defined acceleration he didn’t connect the two ideas He knew that 2 objects fall the same without air resistance but was unable to say why it is so Newton realized that there was a relationship between force and mass producing an acceleration This is known as Newton’s Second Law It states that the acceleration produced by a net force on an object is directly proportional to the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object Isaac Newton Presented by April Senger

  23. More Simply… • Acceleration ~ net force mass • a = F/m or F = m·a • Notice that if the mass is doubled the force required would be doubled to have the accerlation remain the same • If the force is doubled (mass stays the same), the acceleration doubles Presented by April Senger

  24. Concept Check • If you push on a shopping cart it will accelerate… • If you push five times harder, what happens to the acceleration? • If you push the same, but the cart is loaded so that it has five times as much mass, what happens to the acceleration? • If you push five times harder when it is loaded with five times as much mass, what happens to the acceleration? Presented by April Senger

  25. Calculate This… • If you have a 1000 kg car pulled by a cable with 2000 N of force. What will be the acceleration of the car? • Answer: 2 m/s2 • Remember… N is kg·m/s2 • Suppose the force is 4000 N. What would the acceleration be? • 4 m/s2 Presented by April Senger

  26. Friction • Friction always works in the opposite direction of the motion • Friction is contact with something else including solids, liquids or gases • Pulling a box to the right results in friction pulling left, swimming to the West pulls you to the East, and falling towards the Earth air friction pushes you up • The amount of friction depends on what the substances are made of Presented by April Senger

  27. Flying High • If you are in an airplane that is flying with a constant speed of 900 km/h and the thrust of the engines is a constant 80,000 N, what is the acceleration of the airplane? • Answer: 0 because the velocity is constant • What is the combined force of the air resistance that acts all over the plane’s surface? • Answer: 80,000 N If it were less the plane would speed up and if it were more it would slow down Presented by April Senger

  28. About to Brake? • Older cars did not have ABS or Anti-Lock (automatic) breaking systems • There is two kinds of friction…Sliding and Static Friction • What is the advantage of ABS over traditional stopping friction (sliding)? Presented by April Senger

  29. Concept Check • Two forces are acting on a bowl resting on a table: the bowl’s weight and the support force from the table. Does a force of friction also act on the bowl? • Suppose a jumbo jet is flying with a constant velocity when the thrust of its engines is a constant 80,000 N. What is the acceleration of the jet? What is the force of air drag acting on the jet? Presented by April Senger

  30. Free Fall • Galileo started by working with balls rolling down a plane to slow the speed • Measuring accurate time for vertical falls was not as easy as it is today • He did notice that as the plane became steep, the ball accelerated faster • When an object is falling and only the force of gravity is acting on it is called Free Fall • Forces such as air drag is neglected Presented by April Senger

  31. Aristotle, Galileo & Newton Again • Mass doesn’t have an effect on free fall • Remember, a 1 kg object and 10 kg object will hit the ground at the same time (Galileo) • Aristotle thought that the 10 kg object would be 10 times faster • Galileo couldn’t say why the accelerations were equal • We explain this with Newton’s Second Law Presented by April Senger

  32. Givens: a = ? m = 1 kg F = m x 9.8 (basically 10) a = 10 N / 1 kg a = 10 m/s2 Givens: a = ? m = 10 kg F= 10 kg x 10 m/s= 100N a = 100 N / 10 kg a = 10 m/s2 Gravity is 9.8 m/s2 (10) & a = F / m Presented by April Senger

  33. What about Air Friction? • Air resistance isn’t noticeable on objects such as rocks • Feathers and coins would have a noticeable change in air • In a vacuum they would accelerate the same Presented by April Senger

  34. A 5 kg bag of sand has a weight of 50 N. When dropped its acceleration is… a = 50 N/ 5 kg = ? m/s2 A 10 kg bag of sand has a weight of 100 N. when dropped its acceleration is… a = ___ / 10 kg = ? m/s2 Calculate the free fall acceleration of a 20 kg bag of sand. a = ___ / ___ = ? m/s2 The answer to all of these is 10 m/s2 Practice Presented by April Senger

  35. What Can Change the Acceleration of a Fall? • Most times, air drag is not negligible for falling objects • The two factors with the most impact are surface area and speed • As you fall for longer periods of time, your air drag builds up as speed increases resulting in reduced acceleration • A flying squirrel has more surface area thus slowing the acceleration Presented by April Senger

  36. Terminal Speed or Velocity • The net force down is an object’s weight • The force pushing up is air drag • An object will continue to accelerate until the weight pulling down is equal to the air drag pushing up • The object continues to move a constant speed and no longer accelerates • This is called Terminal Speed or Velocity Presented by April Senger

  37. Why Use Parachutes? • Humans reach terminal speed between 150-200 km/h • When you use a parachute, there is much more surface area • The pull down is rapidly equaled by the drag up • A parachute will reach terminal speed at 15-25 km/h allowing a safe landing Presented by April Senger

  38. Concept Check… • Two parachutists (one heavy and one light) jump from the same altitude with parachutes of the same size • Which person reaches terminal speed first? • Which person has the greatest terminal speed? • Which person gets to the ground first? • If there were no air drag, like on the moon, how would your answers to these questions differ? Presented by April Senger

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