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