L2 Forces, Mass, Acceleration, Pressure, Review of Exponents

Distance When an object moves, it goes from point A to point B – that is the DISTANCE it traveled. (SI unit is the meter) Distance is how much ground an object has covered during its motion. A B

Displacement Knowing how far something moves is not sufficient. You must also know in what direction the object moved. Displacement is how far our of place the object is; it is the object’s overall change in position.

Speed Calculating Speed: If you know the distance an object travels in a certain amount of time, you can calculate the speed of the object. Speed = Distance/timeAverage speed = Total distance/Total time What is instantaneous speed? Instantaneous speed is the velocity of an object at a certain time.

Because velocity depends on direction as well as speed, the velocity of an object can change even if the speed of the object remains constant. Velocity 2.1 Describing Motion The speed of this car might be constant, but its velocity is not constant because the direction of motion is always changing.

Velocity Velocity is a description of an object’s speed and direction. As the sailboat’s direction changes, its velocity also changes, even if its speed stays the same.

Speed v. Velocity 1.How are speed and velocity similar? They both measure how fast something is moving 2. How are speed and velocity different? Velocity includes the direction of motion and speed does not (the car is moving 5mph East) 3.Is velocity more like distance or displacement? Why? Displacement, because it includes direction.

Graphing Speed DISTANCEDISTANCE T I M E Speed constant Object is stopped Object is moving at a different (lower) speed

The steepness of a line on a graph is called slope. The steeper the slope is, the greater the speed. A constant slope represents motion at constant speed. Using the points shown, the rise is 400 meters and the run is 2 minutes. To find the slope, you divide 400 meters by 2 minutes. The slope is 200 meters per minute.

Problem Solving: Calculating Speed What is the speed of a sailboat that is traveling 120 meters in 60 seconds? Step 1: Decide what the problem is asking? A boat traveled 120 meters in 60 seconds. What was the speed of the boat? Step 2: What is the equation to calculate speed? Speed = Distance/Time Step 3: Solve the problem using the equation: Speed = 120 meters 60 seconds = 2 m/s So, the boat was traveling at 2 m/s Now you try: What is the speed of a car that is traveling 150 miles in 3 hours?

Answer: Step 1: What are the facts in the problem? A car is traveling 150 miles in 3 hours. Step 2: What is the equation to solve the problem? Speed = Distance/Time Step 3: Solve the problem. Speed = 150 miles 3 hours Speed = 50 miles/hr. So, the car is traveling 50 miles/hr.

Acceleration Acceleration is the rate at which velocity changes. Acceleration can result from a change in speed (increase or decrease), a change in direction (back, forth, up, down left, right), or changes in both.

The pitcher throws. The ball speeds toward the batter. Off the bat it goes. It’s going, going, gone! A home run! Before landing, the ball went through several changes in motion. It sped up in the pitcher’s hand, and lost speed as it traveled toward the batter. The ball stopped when it hit the bat, changed direction, sped up again, and eventually slowed down. Most examples of motion involve similar changes.

You can feel acceleration! If you’re moving at 500mph east without turbulence, there is no acceleration. But if the plane hits an air pocket and drops 500 feet in 2 seconds, there is a large change in acceleration and you will feel that!

Calculating Acceleration Acceleration = Change in velocity Total time So…Acceleration = (Final speed – Initial speed) Time

As a roller-coaster car starts down a slope, its speed is 4 m/s. But 3 seconds later, at the bottom, its speed is 22 m/s. What is its average acceleration? Calculating Acceleration What information have you been given? Initial speed = 4 m/s Final Speed = 22 m/s Time = 3 s

What quantity are you trying to calculate? The average acceleration of the roller-coaster car. What equation contains the given quantities and the unknown quantity? Acceleration = (Final speed – Initial speed)/Time Perform the calculation. Acceleration = (22 m/s – 4 m/s)/3 s = 18 m/s/3 s Acceleration = 6 m/s2 The roller-coaster car’s average acceleration is 6 m/s 2. Calculating Acceleration

Graphing acceleration SPEEDSPEED T i m e Object accele- rates Object moves at constant speed Object decelerates

Now You Try: A roller-coaster’s velocity at the top of the hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s. What is the average acceleration of the coaster?

The slanted, straight line on this speed-versus-time graph tells you that the cyclist is accelerating at a constant rate. The slope of a speed-versus-time graph tells you the object’s acceleration. Predicting How would the slope of the graph change if the cyclist were accelerating at a greater rate? At a lesser rate?

Since the slope is increasing, you can conclude that the speed is also increasing. You are accelerating. Distance-Versus- Time Graph The curved line on this distance-versus-time graph tells you that the cyclist is accelerating.

A car’s velocity changes from 0 m/s to 30 m/s in 10 seconds. Calculate acceleration. Final speed = 30 m/s Initial speed = 0 m/s Time = 10 s Remember (final speed – initial speed) ÷ time is acceleration. (30 m/s – 0 m/s) ÷ 10 s = 30 m/s ÷ 10 s = 3 m/s 2

Frictionless motion Demo

5.NEWTON’S FIRST LAW OF MOTION Newton finished the overthrow of Aristotelian ideas. Law 1 (Law of Inertia) Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. “If you leave an object alone, it has constant velocity.”

Newton's concept of motion said that the natural state of an object was (a) constant velocity (b) constant acceleration (c) constant net force

Inertial mass

We call the change in velocity per unit time the acceleration a= Δv/ Δt The Δv can be in magnitude and/or direction

1.FORCE CAUSES ACCELERATION The combination of forces that act on an object is the net force. (Only the net force is shown in the figures on this slide.) Fa Fa Fa The acceleration of an object is directly proportional to the net force. mmm This symbol means proportional to

 The force in each of these equations represents the vector sum of all of the forces acting on the object of mass m.  Units of force - N and lb or 5. NEWTON’S SECOND LAW OF MOTION

slug)  A slug weighs  Every object possesses inertia (mass).  Inertia is the sluggishness of an object to changes in its state of motion.  Mass - a measure of the inertia of an object (Units - kg and 3.MASS AND WEIGHT 32 lb.  Inertia deals with how hard it is to start and stop an object.

Gravitational Mass

Newton's Law of Universal Gravitation r m1m1 m2m2

2.The Universal Gravitational Constant, G

At earth’s surface, F = G mM e /R e 2 or W = (Gm e/ Re 2 ) m or W=(g)m or weight = mass x acceleration of gravity g = 9.8 m/s 2

A 2 kg mass weighs: A) 2 N B) 19.6 N C) 32 N D) 10 5 N E) Not enough information given

2 Concepts of Mass: Equivalence of gravitational mass and Inertial mass Theory of General relativity

Pressure=Force/contact area On left, the pressure on the bottom block, i.e. the weight of the top block/contact area, is lower than the pressure on the bottom block on the right.

Pressure in a fluid (including air!)

Exponential Notation

1000 = 10 x 10 x 10 = = 10 x 10 = = = = 1/10 = = 1/100 = = 1/1000 = 10 -3

Ordinary decimal notationScientific notation (normalised) 3003×10 2 4,0004×10 3 5,720,000, ×10 9 − −6.1×10 −9

For CAPA, we write 356 as 3.56E2

10 -2 x = /10 6 = 10 -8