Motion, Forces, and Energy

Motion and Momentum

Section 1: What is motion?

All matter is constantly in motion.

Motion involves a change in position…

An object changes position if it moves relative to a reference point. To understand a reference point;

1) Picture yourself standing at the front office

2) Then, you walk to our classroom

3) When you reach our classroom, you have traveled about 50 meters

4) Since the office is where we started, it would be our reference point, because our position has changed 50 meters relative to the starting spot (the office) and motion has occurred

Distance and Displacement

Distance is the total length of the route an object travels when it moves.

Displacement includes distance and direction of the stopping point from the starting point.

SpeedSpeed- the distance traveled divided by the time taken to travel the distance.

Formula for speed: speed (s)= distance (d) / time (t) or s= d/t

The for speed are meters per second (m/s).

An object in motion can change speeds many times as it moves from one point to another, speeding up or slowing down.

Average SpeedAverage speed- equals the total distance traveled divided by the total time taken to travel the distance.

Question: If it takes you 0.5 h to walk 2 km to the library, what is your average speed? We solve this equation by using the s= d/t method:

1) Plug in the numerical digits into the equation2) So, 2 km/0.5 h = ?3) 4 km/h

What is instantaneous speed?

Instantaneous speed- the speed of an object at one instant of time.

How do you graph motion?

Motion can be graphed on a distance-time graph with time plotted on the horizontal axis (x-axis or left to right) and distance plotted on the vertical axis (y-axis or up and down).The steeper the line on a distance-time

graph, the greater the speed.A horizontal line on a distance-time graph

indicates that no change in position is occurring and the speed is 0m/s.

Velocity

Velocity- speed of an object and its direction of motion; velocity changes if either, or both, of these changes. V= displacement (d) / time (t) or V= d/t

Section 2::

Change in Velocity

Each time you take a step you are changing the velocity of your body.

You are probably most familiar with the velocity changes of a moving bus or car.

Acceleration- change in velocity divided by the time for the change to occur; it can include an object’s speeding up, slowing down, and/or changing direction.

Calculating Acceleration

Change in velocity = final – starting

velocity velocity

Acceleration= final speed- starting speed time

Or: a= (sf-si)/t

Acceleration= change in velocity time

Calculating Acceleration (cont’d)

The unit of acceleration is distance divided by time squared; (m/s2).

Acceleration is positive when an object speeds up.

Acceleration is negative when an object slows down.

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph accelerates to90 mph in 3 seconds. What is thecar’s acceleration?

=90 mph - 60 mph

3 seconds

=30 mph

3 seconds

= 10 mph/second

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is thecar’s acceleration?

=0 mph - 60 mph

6 seconds

=- 60 mph

6 seconds

= - 10 miles per hour per second

Graphing AccelerationAccelerated motion can be graphed on a speed-time graph with speed on the vertical axis (y-axis or up and down) and time on the horizontal axis (x-axis or left to right).

An object that is speeding up will have a line on a speed-time graph that slopes upward.

An object that is slowing down will have a line on a speed-time graph that slopes downward.

A horizontal line on the speed-time graph represents an acceleration of zero or constant speed.

PositivePositive acceleration acceleration

Negative Negative accelerationacceleration

- A constant acceleration produces a straight line or

linear slope (rise/run).

- The slope of a velocity-time graph

(rise/run) will predict an objects

instantaneous acceleration.

a = v/t

0 or constant speed

Galileo1600’s

Studied how things fell

Rolled balls down an inclined plane

Found that the speed increased as it rolled down the ramp

Galileo

t = 0t = 1 second

t = 2 seconds

t = 3 seconds

Acceleration= Acceleration= change in velocitychange in velocity timetime

Practice Problem # 1 Calculate the acceleration of a bus whose speed changes from 6 m/s to 12 m/s over a period of 3 seconds.

What do we know: Initial Speed: 6 m/s Final Speed: 12 m/s Time: 3 seconds

Practice Problem # 2 Suppose you were riding your bicycle in a straight line and increased your speed from 4 m/s to 6 m/s in 5 seconds. Calculate your acceleration.

Practice Problem # 3 Suppose you slow down from a speed of 4 m/s to 2 m/s in 5 seconds. Now the final speed is less than the initial speed. Calculate your acceleration.

Section 3: Momentum

Mass and InertiaMass- the amount of matter in an object.The SI unit for mass is the kilogram

Inertia- the tendency of an object to resist a change in its motion.Objects with more mass have more inertia, thus is harder to change its motion

MomentumMomentum- a measure of how difficult it is to stop a moving object; equals the product of mass and velocity.

Momentum is usually symbolized by p

Momentum= mass X velocity orp= mv

Momentum has units of kg multiplied by m/s

Since velocity includes direction, momentum has the same direction as velocity.

Practice Problem 1

Calculate the momentum of a 16-kg bicycle traveling north at 3 m/s.

Practice Problem # 2Calculate the momentum of a 12-kg bicycle traveling east at 2 m/s.