Physics 2.2

Speed and Velocity,
Distance and Displacement:
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Speed is a scalar quantity.
Velocity is a vector quantity.
Distance is a scalar.
Displacement is a vector.

Solve:
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A car begins to ride at 20 m/s north and finishes at 30 m/s north. What is the average velocity?
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Average velocity= initial + final velocity
2

Graphs you should know:
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Distance vs Time
– Slope = ?
Velocity vs Time
– Slope = ?
– Area = ?

Distance vs Time

Velocity vs Time

Velocity vs Time
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We can deduct interesting information from a velocity-time graph: The slope of the line is the acceleration, but the area under the line is the
displacement!
Let's see how to determine the displacement an object undergoes during a given time:

Free Fall:
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Use the Kinematic equations for constant acceleration.
Use 0 m/s for initial and starting velocities, and g for acceleration (-9.81 m/s).
After 1 second of free fall, what is the velocity of an object in free fall? 2 seconds?

Time, Distance, and Velocity of an Object in Free Fall:
Time
0 s
1 s
2 s
3 s
4 s
Distance
Top of Cliff
4.9 m
19.6 m
44.1 m
78.5 m
Velocity v = 0 m/s v = 9.81 m/s v = 19.6 m/s v = 29.4 m/s v = 39.2 m/s

Statics:
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Forces which act on objects
Combined concurrent forces are called the resultant force

Question?
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Two concurrent forces on and object have a maximum resultant of 45 newtons and a minimum resultant of 5 newtons. What is the magnitude of each of these forces?
Solution: find the resultants in the same and opposite directions.
(20 N and 25 N).

Finding the Resultant
Graphically:
1.
2.
Parallelogram method:
1.
2.
Draw a mirror image of the two force vectors opposite them.
Measure the resultant.
Triangle method:
1.
2.
Draw the second force vector from the head of the first.
Measure the resultant.

Parellelogram

Triangle-method

Equilibrium
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Static equilibrium:
– An object at rest.
Dynamic equilibrium:
– An object with the net forces acting on it are equal to zero. Ex/ an object in free fall that has reached terminal velocity.

Free body diagram

1.
2.
3.
Sir Isaac Newton’s Three
Laws:
An object in motion tends to stay in motion, unless acted upon by a force.
When a force acts on an object, it will accelerate in the direction of that force
When a force acts upon and object, that object will act with and equal and opposite force.

More…
1.
2.
3.
Law of Inertia.
F = ma
F
12
= F
21

???
1.
Which object has the most inertia?
1.
2.
3.
A 0.1 kg baseball travelling 20 meters/second.
A 10 kg sled at rest.
A 5 kg bowling ball traveling 3 meters/ second.

???
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An 8 N force is applied to a 4 kg block on a frictionless table. What is the magnitude of the block’s acceleration?
F = ma
2 m/s²

???
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Which unit is equivalent to a newton per kg?
1. m/s²
2. W/m
3. j·s
4. kg·m/s

Projectile moving
Horizontally:
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When an object is thrown from a height, there is both a horizontal and vertical component.
Find time in the air with: d y
= v i t + ½at²

???
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A baseball is thrown horizontally at 25 m/s from a cliff 45 meters above the level ground. How far from the base of the cliff does the ball hit the ground?
d x
= v x t d y
= v i t + ½at²

A Projectile fired at an
Angle:
1.
2.
Set up two sets of data:
1.
Horizontal component x;
2.
Vertical component y;
Use the kinematic equations to solve for both the horizontal and vertical components.

???
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A ball is thrown in the air at a 30˚ angle from the horizontal at a speed of
100 m/s. Find:
– Time in the air
– Max height
– range

Circular Motion
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Centripetal acceleration
– a = v²/r
Centripetal force
– F = mv²/r

???
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A 2.0 E3 kg car travels at a constant speed of 12 m/s around a circular curve of radius 30. meters.
– What is the magnitude of the centripetal acceleration of the car as it goes around the curve?
– What direction is the centripetal force directed?

Newton’s Universal Law of Gravity
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F = Gm1m2/r²
Weight = mg

Friction
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Static friction: object is not moving
– Fs = Us x Fn
Kinetic friction: object is moving
– Fk = Uk x Fn

Impulse and momentum
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Impulse is the change in momentum.
– J = Ft = ∆p
Momentum is mass x velocity.
– p = mv

A Simple pendulum:
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Does mass effect the period?

More pendulum stuff: