Chapter 3: Newton’s Second Law of motion- Force and acceleration

3.1 Galileo developed the concept of acceleration Founded the concept of acceleration A ball rolling down a hill speeds up Velocity increased by a given amount each second Acceleration: change in speed, a change in direction, or a change in both speed and direction 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 Speeding up in a car The car is changing direction = change in velocity

3.1 Acceleration continued Example Problems: In 1 second, we steadily increase our velocity from 30 km/h to 35 km/h. In the next second, we go from 35 km/h to 40 km/hr, and so on. What is the acceleration? You do an experiment and drop an apple from your head. The object is in free fall and you determine that the free fall’s velocity if 10 m/s in one second. What is the accerleration?

3.2 Force Causes Acceleration Any object that accelerates is acted on by a push or pull of some kind Suppose you pull a toy wagon with a net force of 20N. Then you doubled the net force with 40 N. What happens with the acceleration? If net force doubled, then so is acceleration Acceleration is directly proportional to the net force. Acceleration ~ net force The direction of acceleration is always in the direction of the net force Force in same direction as motion = speed increase Force in opposite direction as motion = speed decrease Force at right angles, change direction of the object Means: Directly proportional

Concept check If you push on a shopping cart, it will accelerate. If you apply four time the net force, how much greater will the acceleration be? If the net force acting on a sports car is reduced to half, how will the acceleration change?

Mass is a measure of inertia Mass of an object relates to inertia EX: full can of rocks vs. empty can Greater the mass, the greater its inertia Mass is also a measure of how much material an object measures Mass depends on the number and kinds of atoms making up the object Lead: made up of many tightly packed atoms so it has a greater volume

Mass is not volume Volume: measure of space Measured in cubic centimeters, cubic meters, or liters Mass is measured in kilograms Ex: equal-size bags of popcorn and jelly beans may have equal volumes but very unequal masses

Mass is not a weight Mass: measure of the amount of matter in an object and depends in its number and kind of atoms Also measure of inertia that an object shows when trying to change its state of motion Weight: Force that depends on gravity Mass doesn’t change depending on gravity Although they are different they are directly proportional to one another Object with great mass has a great weight

Concept check Does a 2-kilogram iron block have twice as much inertia as a 1-kilogram iron block? Twice as much mass? Twice as much volume? Twice as much weight when weighed in the same location? Does a 2-kilogram iron block have twice as much inertia as a 1-kilogram bunch of bananas? Twice as much mass? Twice as much volume? Twice as much weight when weighed in the same inertia? How does mass of a bar of gold vary with location?

1 kilogram weighs 10 Newtons Standard unit of mass is kilograms A 1 kilogram bag of material has a weight of about 10 Newtons Want to know how much something weighs, do 10 times the kg Weight and mass are proportional Precision is needed sometimes EX: 1 kilogram of matter actually weighs 9.8 N. 1 kilogram weighs 2.2 lbs. 2.2 lbs. = 4.45 N

Concept check Why is it okay to say a 1 kg bag of sand weighs 10 N, but a 1 kg. bag of gold weighs 9.8 N? Don’t they weigh the same?

Mass Resists Acceleration Massive objects are more difficult to accelerate Same force and twice as much mass = half as much acceleration Acceleration produced by a given force is inversely proportional to the mass Acceleration ~ 1 𝑚𝑎𝑠𝑠 Inversely: Two values change in opposite ways One value gets larger, the other gets smaller

Concept check Suppose you are 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 a 8 kg. Which cart will accelerate more? How much greater will the acceleration be?

Newton’s Second Law Links Force, Acceleration, and Mass Isaac Newton was the first to realize the connection between force and mass when creating acceleration Newtons Second Law states: “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.” Acceleration = 𝑁𝑒𝑡 𝐹𝑜𝑟𝑐𝑒 𝑀𝑎𝑠𝑠 a= 𝐹 𝑚

Concept check Consider a 1000 kg car pulled by a cable with 2000 N of force. What will be the acceleration of the car? Suppose the force were 4000 N. What would be the acceleration of the car? If you push on a shopping cart, it will accelerate. If you push the same, but the cart is loaded with groceries so it has five times as much mass, what happens to the acceleration? If you push five times harder on the loaded cart, what happens to the acceleration?

Friction is a force that affects motion Friction: an object tends to rub or rubs against something else Occurs for solids, liquids, and gases Acts in a direction to oppose motion Friction in the air is known as drag Amount of friction depends on the material and how much they are pressed together Ex: sliding a book on the floor vs. down a ramp

Objects in Free fall have equal acceleration Galileo found that planes were tipped to effectively slow down acceleration is greater Free Fall: falling only under the influence of gravity, where other forces such as air drag is neglected Any incline has the same acceleration no matter the mass

Newtons second law explains why objects in free fall have equal acceleration All free falling objects have the same force/mass ratio and undergo the same acceleration at the same location Acceleration due to gravity is represented by (g) Ex: 𝑎= 𝐹 𝑚 = 10𝑁 1 𝑘𝑔 =10 𝑚 𝑠 =𝑔 a= 𝐹 𝑚 = 100 𝑁 10 𝑘𝑔 =10 𝑚 𝑠 =𝑔

Acceleration of fall is less when air drag acts Air drag depends on two things: speed and surface area Increase surface area Slow down speed Terminal Speed: stop accelerating Terminal Velocity: stop accelerating in a certain direction