Chapter 6: Motion in Two Dimensions TWO DIMENSIONAL MOTION.
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Transcript of Chapter 6: Motion in Two Dimensions TWO DIMENSIONAL MOTION.
Trajectory
• After a projectile has been given an initial thrust, if you ignore air resistance, it moves through the air only under the force of gravity.
• Force of gravity is what causes it to curve downward.
• Its path through space is called its trajectory.
PROJECTILE MOTIONPROJECTILE MOTION
• What is a projectile?
– Any object shot through the air
• How does it travel?
– Follows a parabolic path
• Assume weight is the only force acting on it
• EQUATIONS OF MOTION will change…slightly
Range Equation
• If a projectile launches and lands from the same vertical height, we can find the distance traveled in the x by the following:
R = vi2 (sin 2/g
• Notice the angle is doubled and the initial velocity is squared
• The unit for range is meters (m)
NEW EQUATIONS OF NEW EQUATIONS OF MOTIONMOTION
Y directionY direction
vvff = (v = (vii sin sin) - g t) - g t
y = (vy = (vii sin sin) t - 1/2 gt) t - 1/2 gt22
vvff22 = (v = (vi i sinsin))
22 - 2 g - 2 g y
X directionX direction
vvff = v = vii
x = vx = vii (cos (cos) t) t
Projectiles launched at an angle…
• When a projectile is launched at an angle, the initial velocity has a vertical component as well as a horizontal component.
• Equations of motions change slightly…now we have to differentiate between x and y components.
Centripetal AccelerationCentripetal Acceleration
• “center seeking”• The acceleration on an
object to keep it traveling in a circular path
• The direction is always pointed towards the center, perpendicular to the velocity.
ac=v2/r
Centripetal ForceCentripetal Force
• Force required to keep an object traveling in circular motion:
Fc = mac = mv2/r• Remove force, will travel
in a straight line• This is different than the
“fictional” force of centrifugal force…which does not exist.
CENTRIPETAL CENTRIPETAL LABLAB
Materials– String/
stopper– Stopwatch– Meter stick– Balance
Procedures– Measure m, r, and t of
the slowly, spinning block
– Calculate v, ac, and Fc.– Repeat using 2
different radii.
51. 28.9 m53. 3.2 m56. 31 m, 212 m58. 14.3 s, 497 m60. 11.8 m/s 61. 9.65 m/s2; 5937 N62. 71 m/s2, 500 N65. 18 m/s67. 1,470 m
Ch6 Ch6 HomeworkHomework
PERIODIC MOTION
• Review hw problems• What is periodic
motion?• Centripetal force is a
“fictional” force• pendulums(equation) • circular motion
PENDULUM LAB
• Each group needs:– pendulum
– stop watch
– meter stick
• measure the difference in T for 5 different lengths of string
• use 10,20,30,40,50 cm• lengths
Egg Drop Egg Drop ParachuteParachute
Rules• Nothing added to egg to
improve its strength• Raw, chicken eggs only• Less than 1 m from egg
bottom to parachute top• Cannot be attached to
anything on the ground or building (i.e. freefalling)
• Must fit through the “fire escape” (the window)
• Nothing attached to the egg to protect it…the egg must hit the ground first
• One throw per group
Eggcellent Eggcellent ParachuteParachute
ProjectProject
Procedures• Ensure the parachute is
working properly…make any adjustments
• Egg must be inspected before attaching to parachute (any cracks and/or rule violations)
• Attach egg to parachute• Egg/parachute must be
inspected again• 1 person from each group will
stay in the class to drop the egg/parachute
• Other group members will be in the courtyard
• After each drop, I will inspect the egg for damage