Motion

Chapter 2

Study of Motion In

Overview:

Motion includes the

relationships of :

• Frame of reference,

• Speed,

• Velocity,

• Acceleration,

• Momentum.

Study of Motion In

Overview:

• Components of motion:

• speed,

• direction.

• Measuring motion requires a unit of distance

and time.

Study of Motion In

Overview:

• Motion is a change in position relative to a

frame of reference.

• Frame of reference is the object or point from

which movement is determined.

• All motion, like time has no relevance without

a frame of reference.

Study of Motion In

Overview:

• In reality, everything is in motion.

• We are spinning on the Earth at a speed of 1300 km (800

miles)/hour

• Earth circles the Sun at 107,400 km (66,600 miles)/hour

• The Sun is moving toward the star Vega at 20 km (12

miles)/second and circling the center of the Milky Way galaxy at

250 km/second (558,000 miles/hr)

• Milky Way is on a collision course with Andromeda galaxy and

both are being pulled into the Virgo cluster 50 million light-years

away.

• And if that isn’t enough, the Virgo cluster (et al.) is being tugged

toward the Great Attractor at 600km/second.

Study of Motion In

Overview:

Movement can be measured only

with reference to something that is

assumed to be fixed.

Speed:

• Speed (v) is the distance traveled by a moving

object per unit of time. It is scalar and does NOT

need a defined direction.

• average speed = change in distance

change in time

or

vav = Δd/ Δt

Δ (delta) = change in where Δd = df - di Δt = tf - ti

Example #1

• What is the speed of a jet that flies 7200 km in 9 hours?

vav = Δd

Δt

= 7200km

9 hr

= 800 km/hr

Example #2

How far would a cruise ship moving at a speed of 50 km/hr travel in 14 hours? vav = Δd

Δt

Δd = (vav)(Δt)

=(50 km/hr )(14 hrs)

= 700 km

Speed:

• Constant Speed is speed that does not change with time.

• Constant speed is always graphed as a straight line.

i.e. Distance traveled is directly proportional to the

time interval passed.

Directly proportional - as one amount increases, another amount increases

at the same rate

Speed:

A steep slope illustrates a fast speed.

A shallow slope indicates a slow speed.

• Instantaneous speed is speed at an instant in time.

• A device such as a speedometer measures instantaneous speed.

Average speed traveled on a highway that is less than the speed limit will not prevent a citation for speeding if the officer’s radar measures an instantaneous speed greater than the speed limit.

Speed:

Practice Problem 1

A passenger elevator travels from the first floor to the

60th floor, a distance of 210m, in 35s. What is the

elevator’s speed?

Practice Problem 2

A motorcycle is moving at a constant speed of 40

km/h. How long does it take the motorcycle to travel a

distance of 10 km?

Practice Problem 3

How far does a car travel in 0.75 h if it is moving at a

constant speed of 88 km/h?

Practice Problem 4 A long-distance runner is running at a

constant speed of 5 m/s. How long does

it take the runner to travel 1 km?

Velocity:

• Velocity is a vector and must include orientation.

• i.e. Velocity is speed in a given direction.

• Velocity can change with constant speed.

• Velocity can be additive or subtractive in relation to an objects medium. • e.g. A fish swimming downstream at 10 km/hr is actually

moving at 15 km/hr if the stream velocity is 5 km/hr

• A rocket launched in the same direction as the Earth rotates has its speed increase ~1500 km/hr

Momentum:

• All moving objects have momentum.

• Momentum of a moving object is directly proportional to its mass. • i.e. Momentum = mass times velocity

or p=mv

• where:

p = momentum (g.km/hr)

m = mass (g)

v = velocity (km/hr)

Momentum: • e.g. A 500-gram object moving at 2km/hr collides

with a 50-gram object. The 500-gram object is stopped. What is the speed of the 50-gram object?

• Step 1. Calculate the momentum of the 500-gram object.

500 g x 2km/hr

= 1000g.km/hr

• Step 2. Calculate the speed of the 50-gram object based on both having equal momentum.

1000 g.km/hr =

50 g

20km/hr

Practice Problem 1

What is the momentum of a car with a

mass of 1300 kg travelling north at a speed

of 28 m/s?

Practice Problem 2 A baseball has a momentum of 6.0 kg•m/s

south and a mass of 0.15 kg. What is the

baseball’s velocity?

Practice Problem 3

Find the mass of a person walking west

at a speed of 0.8 m/s with a momentum of

52.0 kg•m/s west.

Practice Problem 4 The mass of a basketball is three times

greater than the mass of a softball. Compare

the momentums of a softball and a

basketball if they both are moving at the

same velocity.

Acceleration:

• Acceleration is the rate of change in velocity

• acceleration = final velocity – initial velocity

change in time

• or aav = vf – vi

Δt

• or aav = Δv/ Δt

Acceleration:

• Acceleration is measured in meters/second/second

change in V change in t

or m/s2

• Therefore, velocity must be in meters/second and time must be in seconds.

• If an object is slowing down (decelerating) the numerator will be negative.

• This is often referred to as negative acceleration.

Acceleration:

• A distance-time graph for acceleration is

always a curved line.

Distance

Time

Acceleration:

• Q. A roller coaster has a velocity of 10 m/s at the top of a hill. Two seconds later it reaches a velocity of 20 m/s. What is its acceleration?

• aav = vf – vi = 20 m/s - 10 m/s =

Dt 2s

10 m/s = 5 m/s2

2s

Circular Motion:

• Acceleration is a change in velocity

• Since velocity includes direction, an object in circular motion is accelerating even though its speed may remain constant.

• Centripetal Acceleration is acceleration directed toward the center of a circular path.

• The term centripetal is derived from the Greek terms centrum (“center”) and petere (“seeking”).

Circular Motion:

• We will return to the subject of centripetal

acceleration when we discuss forces.

Law of Conservation of

Momentum:

• The total momentum of any group of objects

remains the same unless outside forces act

on the objects.

• i.e. The momentum of an object striking

another object is not lost; it is transferred.

• e.g. A billiard cue ball’s momentum is

transferred to another ball when they collide.