Download Vectors and Scalars

Physical Science STP Physics Study Guide
Position is Relative
Something’s position only has meaning in relation to other objects. You are standing 10 meters from
Steve. We are 3 meters off of the ground. The object being used as the comparison is called the
reference point. In these examples, Steve and the ground are reference points.
Motion is Relative, too.
If a person is walking toward the front of a bus, that person is moving at different speeds relative to the
bus, the ground, and the sun.
Vectors and Scalars
Scalars tell us the magnitude (size) of something. A person may have size 10 shoes, a swimmer may
complete a race in 27.8 seconds, and a car may be moving at 50 mph. All of these numbers are scalars.
Vectors are scalars plus direction. Sometimes it does not make sense to include direction. If you go into
a shoe store, you don’t say, “I’d like to try this on in a Size 10 West.” With some quantities, it may be
helpful or necessary to include direction. As long as you’re going the correct way on the road, a police
officer doesn’t care what direction you are traveling if you are going 50 mph in a 35 mph zone – you are
speeding, regardless. A scalar quantity is all you need. However, your GPS needs to know your speed
and direction to keep track of your progress on a trip. Your GPS needs a vector: You are traveling 50
mph West.
Acceleration
Acceleration (change in velocity) occurs in three situations:
1) speeding up, 2) slowing down, 3) changing direction.
Distance, Speed, and Time
Scalar
Vector
I am measured in these
units.
I am how fast
_______changes.
Equations
Distance
Speed
Displacement
Velocity
m km ft
m/s km/hr
---------------------distance / displacement
d=st
s=d/t
speed / velocity
-----------------------
a = Δs / Δt
F = ma
Acceleration
Force
m/s2
km/hr/s
N
Average Speed
Find the average speed by first finding the total distance traveled and the total time. Then, divide using
the average speed equation: v = d / t.
Example: John is on a trip to San Diego. He drives for 3 hours and goes 180 miles. He then stops for
lunch for 1 hours. John then finishes the final leg of 300 miles in 4 hours. What is John’s average speed?
Add up the distances of the three legs: 180 miles + 0 miles + 300 miles = 480 miles
Add up the times of the three legs:
3 hours + 1 hour + 4 hours = 8 hours
v = d / t = 480 / 8 = 60 miles/hr (mph)
Forces
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Forces are measured in units called Newtons (after Isaac Newton).
Forces are vectors; they have direction and magnitude: 20 N Left
If more than one force acts on an object, then the forces must be resolved (combined).
If two forces act in the same direction, add them together.
If two forces act in opposite directions, subtract them. The direction is of the larger force.
A net force (unbalanced forces) causes the acceleration (change of speed) of an object.
If forces are balanced, then no acceleration occurs (the object’s speed is constant).
Examples
One person pushes left on a cart with a force
of 30 N. Another person pushes right with a
force of 70 N. What is the net force?
Since the forces are in opposite directions, subtract
the forces: F = 70 – 30 = 40 N Since the larger force
is to the right, the resultant net force is 40 N Right.
Two people work together pushing a cart to
the right, with forces of 50 N and 80 N. What
is the net force?
Since both forces are in the same direction,
add the forces: F = 50 + 80 = 130 N Right
Distance vs. Time Graphs
Features to look for:
1) The slope of the line is the speed. A steeper line means that the object is moving faster.
2) If the line is rising to the right, then the object is moving away from your point of reference.
If the line is falling to the right, then the object is going toward your point of reference.
3) A straight line means that the object is moving at a constant speed.
A curved line means that the object is accelerating (changing speed).
Constant speed
Constant Speed
Constant Speed
Changing Speed
No motion
Slow motion
Faster Motion
Acceleration
Newton’s Second Law
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The relationship between force, mass, and acceleration is governed by: F = ma
If the mass is constant, if the force increases, the object accelerates faster.
If the mass is constant, if the force decreases, the object accelerates slower.
If the force is constant, if the mass increases, acceleration decreases.
If the force is constant, if the mass decreases, acceleration increases.
If the acceleration is constant, if the mass increases, the force must also increase.
If the acceleration is constant, if the mass decreases, the force must also decrease.
Examples
A 70-N force is applied to a 10-kg object.
What is the acceleration of the object?
F = ma
70 = 10 a
a = 7 m/s2
A boy applies a force to a brick, accelerating it.
He applies the same force to a much larger brick.
How will the accelerations of the bricks compare?
Since the larger brick has more mass, it will
accelerate more slowly than the smaller brick.
Density and Buoyancy
Calculating Density:
d=m/v
d = density
m = mass
v = volume
Example:
A 36-g object displaces 9 mL of water when submerged. Find the density of the object.
Solution:
The mass of the object is 36 g. The volume of the object is the amount of water displaced, so the
volume is 9 mL. Plugging these numbers into the equation:
d=m/v
d = 36 / 9 = 4 g / mL
Buoyancy Key Facts:
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Water pressure is due to the weight of the water above an object. So, water pressure increases
with depth.
Sink or Float? An object will float if its density is less than that of the fluid. An object will sink if
its density is greater than that of the fluid.
The buoyant force acts in a direction opposite to gravity. Archimedes Principle: The buoyant
force is equal to the weight of the fluid displaced.
Sink or Float? An object will float if the buoyant force is greater than the object’s weight. An
object will sink if its weight is greater than the buoyant force.