Physics 2.2Physics 2.2

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

Solve:Solve:

A car begins to ride at 20 m/s A car begins to ride at 20 m/s north and finishes at 30 m/s north and finishes at 30 m/s north. What is the average north. What is the average velocity?velocity?

Average velocity= Average velocity= initial + final velocityinitial + final velocity

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Graphs you should Graphs you should know:know: Distance vs TimeDistance vs Time

– Slope = ?Slope = ? Velocity vs TimeVelocity vs Time

– Slope = ?Slope = ?– Area = ?Area = ?

Distance vs TimeDistance vs Time

Velocity vs TimeVelocity vs Time

Velocity vs TimeVelocity vs Time

We can deduct interesting information from a We can deduct interesting information from a velocity-time graph: The slope of the line is velocity-time graph: The slope of the line is the acceleration, but the area under the line the acceleration, but the area under the line is the is the displacementdisplacement! !

Let's see how to determine the displacement Let's see how to determine the displacement an object undergoes during a given time:an object undergoes during a given time:

Free Fall:Free Fall:

Use the Kinematic equations for Use the Kinematic equations for constant acceleration.constant acceleration.

Use 0 m/s for initial and starting Use 0 m/s for initial and starting velocities, and g for acceleration (-9.81 velocities, and g for acceleration (-9.81 m/s).m/s).

After 1 second of free fall, what is the After 1 second of free fall, what is the velocity of an object in free fall? 2 velocity of an object in free fall? 2 seconds?seconds?

Time, Distance, and Time, Distance, and Velocity of an Object in Velocity of an Object in Free Fall:Free Fall:TimeTime

0 s0 s

1 s1 s

2 s2 s

3 s3 s

4 s4 s

DistanceDistance

Top of CliffTop of Cliff

4.9 m4.9 m

19.6 m19.6 m

44.1 m44.1 m

78.5 m78.5 m

VelocityVelocity

v = 0 m/sv = 0 m/s

v = 9.81 m/sv = 9.81 m/s

v = 19.6 m/sv = 19.6 m/s

v = 29.4 m/sv = 29.4 m/s

v = 39.2 m/sv = 39.2 m/s

Statics:Statics:

Forces which act on objectsForces which act on objects Combined concurrent forces are Combined concurrent forces are

called the resultant forcecalled the resultant force

Question?Question?

Two concurrent forces on and Two concurrent forces on and object have a maximum resultant object have a maximum resultant of 45 newtons and a minimum of 45 newtons and a minimum resultant of 5 newtons. What is resultant of 5 newtons. What is the magnitude of each of these the magnitude of each of these forces?forces?

Solution: find the resultants in the Solution: find the resultants in the same and opposite directions. same and opposite directions.

(20 N and 25 N).(20 N and 25 N).

Finding the Resultant Finding the Resultant Graphically:Graphically:

1.1. Parallelogram method:Parallelogram method:1.1. Draw a mirror image of the two force Draw a mirror image of the two force

vectors opposite them. vectors opposite them.

2.2. Measure the resultant.Measure the resultant.

2.2. Triangle method:Triangle method:1.1. Draw the second force vector from the Draw the second force vector from the

head of the first.head of the first.

2.2. Measure the resultant.Measure the resultant.

ParellelogramParellelogram

Triangle-methodTriangle-method

EquilibriumEquilibrium

Static equilibrium:Static equilibrium:– An object at rest.An object at rest.

Dynamic equilibrium:Dynamic equilibrium:– An object with the net forces acting An object with the net forces acting

on it are equal to zero. Ex/ an object on it are equal to zero. Ex/ an object in free fall that has reached terminal in free fall that has reached terminal velocity.velocity.

Free body diagramFree body diagram

Sir Isaac Newton’s Sir Isaac Newton’s Three Laws:Three Laws:

1.1. An object in motion tends to stay in An object in motion tends to stay in motion, unless acted upon by a force.motion, unless acted upon by a force.

2.2. When a force acts on an object, it will When a force acts on an object, it will accelerate in the direction of that accelerate in the direction of that forceforce

3.3. When a force acts upon and object, When a force acts upon and object, that object will act with and equal that object will act with and equal and opposite force.and opposite force.

More…More…

1.1. Law of Inertia.Law of Inertia.

2.2. F = maF = ma3.3. FF1212 = F = F2121

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1.1. Which object has the most Which object has the most inertia?inertia?

1.1. A 0.1 kg baseball travelling 20 A 0.1 kg baseball travelling 20 meters/second.meters/second.

2.2. A 10 kg sled at rest.A 10 kg sled at rest.

3.3. A 5 kg bowling ball traveling 3 meters/ A 5 kg bowling ball traveling 3 meters/ second.second.

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An 8 N force is applied to a 4 kg An 8 N force is applied to a 4 kg block on a frictionless table. block on a frictionless table. What is the magnitude of the What is the magnitude of the block’s acceleration?block’s acceleration?

F = maF = ma 2 m/s2 m/s²²

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Which unit is equivalent to a Which unit is equivalent to a newton per kg?newton per kg?

1.1. m/sm/s²²

2.2. W/mW/m

3.3. j·sj·s

4.4. kg·m/skg·m/s

Projectile moving Projectile moving Horizontally:Horizontally: When an object is thrown from a When an object is thrown from a

height, there is both a horizontal height, there is both a horizontal and vertical component. and vertical component.

Find time in the air with:Find time in the air with:

ddyy = v = viit + t + ½at²½at²

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A baseball is thrown horizontally A baseball is thrown horizontally at 25 m/s from a cliff 45 meters at 25 m/s from a cliff 45 meters above the level ground. How far above the level ground. How far from the base of the cliff does the from the base of the cliff does the ball hit the ground?ball hit the ground?

ddxx = v = vxxtt ddyy = v = viit + t + ½at²½at²

A Projectile fired at an A Projectile fired at an Angle:Angle:

1.1. Set up two sets of data:Set up two sets of data:1.1. Horizontal component x;Horizontal component x;

2.2. Vertical component y;Vertical component y;

2.2. Use the kinematic equations to Use the kinematic equations to solve for both the horizontal and solve for both the horizontal and vertical components.vertical components.

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

Circular MotionCircular Motion

Centripetal accelerationCentripetal acceleration– a = va = v²/r²/r

Centripetal forceCentripetal force– F = mvF = mv²/r²/r

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A 2.0 E3 kg car travels at a A 2.0 E3 kg car travels at a constant speed of 12 m/s around a constant speed of 12 m/s around a circular curve of radius 30. meters. circular curve of radius 30. meters. – What is the magnitude of the What is the magnitude of the

centripetal acceleration of the car as centripetal acceleration of the car as it goes around the curve?it goes around the curve?

– What direction is the centripetal force What direction is the centripetal force directed?directed?

Newton’s Universal Newton’s Universal Law of GravityLaw of Gravity

F = Gm1m2/rF = Gm1m2/r²² Weight = mgWeight = mg

FrictionFriction

Static friction: object is not Static friction: object is not movingmoving– Fs = Us x FnFs = Us x Fn

Kinetic friction: object is movingKinetic friction: object is moving– Fk = Uk x FnFk = Uk x Fn

Impulse and Impulse and momentummomentum Impulse is the change in Impulse is the change in

momentum.momentum.– J = Ft = J = Ft = ∆p∆p

Momentum is mass x velocity.Momentum is mass x velocity.– p = mv p = mv

A Simple pendulum:A Simple pendulum:

Does mass effect the period?Does mass effect the period?

More pendulum stuff:More pendulum stuff: