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Ch. 7Forces and Motion in Two
Dimensions
Milbank High School
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Sec. 7.1Forces in Two Dimensions
Objectives Determine the force that produces equilibrium
when three forces act on an object Analyze the motion of an object on an inclined
plane with and without friction
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What is meant by two dimensions?
Consider a golf ball being hit out of a sandtrap It has a horizontal force AND a vertical force We can solve for many different things using
a combination of forces and vectors Height of the ball
Time in the air Velocity when it hits the ground
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Equilibrant
A force exerted on an object to produceequilibrium
Same magnitude as the resultant force butopposite in direction
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Solving problems in twodimensions
Draw it out! Rearrange vectors to form a triangle if
possible Solve for the resultant vector
Opposite in direction
Example Problem Pg. 151
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Sec. 7.2Projectile Motion
Objectives Recognize that the vertical and horizontal
motions of a projectile are independent Relate the height, time in the air, and the
initial velocity of a projectile using its verticalmotion, then determine the range.
Explain how the shape of the trajectory of amoving object depends upon the frame of reference from which it is observed.
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Projectiles have independentmotions!
Projectiles have two velocities, one in thex direction, and one in the y direction
x is always constant y will be changing due to the acceleration
due to gravity
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Velocity of projectiles launchedhorizontally
vx = initial velocity vy = (-g)t
v = resultant velocity vector
Example Pg. 157
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Effects of air resistance
We ignore the effects of air resistance for these problems
Sometimes it would make a largedifference, other times it wouldnt
Many projectiles modified so that theyreduce air resistance
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Projectiles launched at an Angle
Usually given angle of launch and velocity What do we have to find?
Maximum height Range
Horizontal distance
Flight time hang time
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Projectiles Launched at an Angle
Two initial velocity components vxo
vyo
How do we find these?
vx = v o(cos )vy = v o(sin )
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Projectiles Launched at an Angle
tup = v yo/g ttotal = 2(t up )
Peak Heighty = v yot - gt 2
RangeR = v xot
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Projectiles launched at an Angle
The Flight of a Ball Example Problem Pg. 159
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Sec. 7.3Circular Motion
Objectives Explain the acceleration of an object moving
in a circle at constant speed
Describe how centripetal accelerationdepends upon the objects speed and theradius of the circle
Recognize the direction of the force thatcauses centripetal acceleration
Explain how the rate of circular motion ischanged by exerting torque on it.
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Uniform Circular Motion
Movement of an object at constant speedaround a circle with a fixed radius
Merry-go-round
Circumference = 2*pi*Radius
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Vectors
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Acceleration
Which direction? Always towards
the center
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Centripetal Force
Center seeking Net force towards the center that causes
the object to try to seek the center What force is pulling it in? As a bucket of water istied to a string and spunin a circle, the force of tensionacting upon the bucket providesthe centripetal force required for circular motion.
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Net Force
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Example Problem Pg. 165
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