motion - amazon s3 · circular motion: • acceleration is a change in velocity • since velocity...
TRANSCRIPT
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.