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

2. 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. 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?

4. 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

5. 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?

6. 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

7. 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

8. 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

9. 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?

10. 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

11. 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?

12. 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

13. 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?

14. 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

15. 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?

16. 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

17. 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

18. 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

19. 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