Physics and Honors Physics – Kinematics



Physics – Kinematics

I. Introduction

❖ Motion ( the change in position and/or orientation of an object.

▪ All motion is relative ( that is all objects move w/r/t other objects.

( in order to describe the motion of an object it must be compared to another object.

❖ Kinematics ( the study of HOW things move.

❖ Dynamics ( the study of WHY things move.

Distance vs. Displacement

❖ Position ( the separation between an object and some reference point.

❖ Distance (d, s, r) ( a scalar quantity describing the total path length.

( “how far did you actually travel?”

( think about miles added to the odometer

❖ Displacement (x, y, d, s, r) ( a vector quantity describing the straight line path length between two points.

( “how far are you from where you started”

Examples: running around a track, road trip (total mileage vs. straight line distance), football

II. Speed vs. Velocity

❖ Speed (s, v) ( the average speed of an object is the rate at which a (total) distance is covered in a (total) time period.

( speed is a scalar quantity.

❖ Velocity (v) ( the average velocity of an object is the rate at which an object covers a given displacement.

( velocity is a vector quantity

Instantaneous Speed vs Instantaneous Velocity

Average speed/velocity considers the TOTAL distance/displacement traveled in a TOTAL TIME frame. Instantaneous speed/velocity is the rate at ONE SPECIFIC MOMENT.

Specifically the instantaneous speed/velocity is the rate of change in distance/displacement as the time frame approaches zero ([pic])

Example: speedometer question

Velocity Big topics: narrative of each line segment, calculations off of graph (velocity), what does +/- slope indicate, what does above/below x axis indicate, how to figure out distance and displacement, where is east/west (positive/negative velocity), what does x axis indicate,

Graphing :

|60 | |

| | |

|[pic] [pic] |d = vot + ½at2 |

| | |

| |vf2 = vo2 + 2ad |

| | |

| |[pic] |

V. Free Fall

Example Problem:

A student drops a stone into a well. If the stone splashes into the water 1.0-second after it was dropped, how deep is the well?

The Law of Falling Bodies

NEGLECTING AIR RESTISTANCE, all objects fall with the same rate of acceleration. At sea-level (on Earth) this acceleration is 9.8 m/s2 DOWN (= 32.2 ft/s2).

• The acceleration due to gravity is uniform (for a given location) NO MATTER WHAT THE MASS OF THE OBJECT!!!

• This is NOT the force of gravity…it is the effect of the force of gravity!

History

( early “scientists” (like Aristotle) thought that heavier objects fall at a greater rate than light objects (based on observation of things like a stick verses a leaf). The problem was nobody ever TESTED anything to see if this was always true.

Demo: drop a book and a piece of paper

( GALILEO questioned this idea and designed an experiment to test it. This was the birth of the scientific method!

He HYPOTHESIZED that all bodies would demonstrate the same uniform acceleration when air (drag) was not a factor.

His METHOD was indirect. He couldn’t just time the fall for a falling body because there were no convenient timing methods (like stop watches) in the early 1600s.

He rolled various size/mass balls down a slight incline and would LISTEN for bells to chime.

Demos/examples:

Drop a book and a piece of paper (open) THEN crumple the paper and drop again ( without the air resistance, they fall together.

Drop a tennis ball and a bowling ball

Video: Misconceptions about free fall

Web Clip: Moon Hammer and feather (David Scott August 2, 1971)

Video: Mechanical Universe (Galileo’s experiment)

Calculations: Free fall

You may recall in math:

H = -16t2 when Vo= 0

Where did this equation come from????

H = -16t2 when Vo= 0

d = V0t + ½ at2

Example Problem:

A stone dropped in to a well splashes into the water 1.5 seconds after it is released. How deep is the well?

Strategy – use chart for free fall, throw up, projectiles!!

#1 LIST WHAT YOU KNOW AND WHAT YOURE SOLVING FOR

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

Activity/Demo: Falling Dollar – Reaction Time Demo

Video Link

Dollar bill math explanation:

d = v0t + 1/2at2

since v0 = 0 (starting from rest) d = v0t + 1/2at2

resolve for t t = √(d/[pic]a) or t = √(2d/a)

since the catching fingers are at midway point, the falling distance of the dollar bill is about 8cm or 0.08m

t = √(2d/a)

t = √(2x0.08)/9.8

t = 0.128s

So what’s the big deal.

Most people’s reaction times are between 0.15sec and 0.20 sec, because it takes at least 0.143 seconds for nerve impulses to travel from the eye to the brain to the fingers. So MOST people will JUST miss the dollar!

Remember: Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things:

• whether the object is speeding up or slowing down

• whether the object is moving in the + or - direction

The general principle for determining the acceleation is:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

“Throw Up” Problems

Neglecting Air resistance the motion of an object projected upward is symmetrical!

|GOING UP |TOP |GOING DOWN |

|Object slows |V= 0 |Object gains speed |

|a = 9.8m/s2 DOWN |a = 9.8m/s2 DOWN |a = 9.8m/s2 DOWN |

|mathematically we write this as: | |mathematically we write this as: |

|a = -9.8m/s2 | |a = +9.8m/s2 |

|(acceleration is in opposite direction of gravity) | |(acceleration is in opposite direction of gravity) |

|symmetry to way down | |symmetry to way up |

| |OVERALL MOTION | |

| |dup = ddown | |

| |tup = tdown | |

| |*vup = vdown* | |

Example Problem: A boy throws a ball up with an initial speed of 12.0m/s. He catches it when it falls back down.

#1 what is the max height of the ball?

#2 What is the time to reach this elevation?

#3 what is the total time of the flight?

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

Sample #2 A clown throws a ball vertically upward with an initial speed of 5.5m/s. Determine the following

#1 max height

#2 time to reach the max height

#3 total flight time

#4 speed when the ball reaches his hand

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

Elevated Throw Up

Example: You are launching smarties upward with an initial velocity of 6.5m/s off Catan’s stadium which is 28.0 meters above the ground. How long does it take to reach the ground?

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

*there are other ways to solve this problem where you would break the smarties’ pathway into different segments. However, this method is the easiest for multiple reasons (no quadratic equation, least amount of pathway segments). If you wish to see the other methods, please see me.

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[pic]

[pic]

P

o

s

i

t

i

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n

in

meters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Time (s)

All points along a straight line have the same velocity (which is the same as the average) b/c the slope is uniform.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Time (s)

All points along a straight line have the same instantaneous acceleration (which is the same as the average) b/c the slope is uniform.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Time (s)

[pic]

1 2 3 4 5 6 (time (s)

1 2 3 4 5 6 (time (s)

* you can average instantaneous speeds/velocities. You CANNOT average avg. speeds/velocities

Now…let’s solve the problem using the new equation.

Much easier!

Now…let’s solve the problem using the new equation.

Much easier!

CAREFUL!

When vo =0 it will force you into in the need to use the quadratic formula:

[pic]INSTEAD:

use #1

vf2 = vo2 + 2ad

then use

#2[pic]

The – sign is telling you down (in the math’s equation)

Cancels when

vo = 0

a = 32ft/s2

32 x ½ = 16

The time for the dollar to fall can be determined using a big five (free fall from rest).

8cm

Going Down (&,-.=EMX the object gains speed as it falls so the acceleration is speeding up.

Going up ( the object is losing speed so the acceleration is slowing down.

At the TOP ( it stops so v = 0 m/s

( it is still accelerating so

a = 9.8 m/s2 down

[pic]

[pic]

28 meters

[pic]

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