UEQ

When a object travels through the air, what variables defines its motion

LEQ

What variables define the motion of an object that rolls off the table top?

Chapter 6 Motion in Two Dimensions

Projectile motion : motion in both the vertical (y-axis) and in the horizontal (x-axis).

1. Velocity, acceleration and displacement will occur both

in the horizontal and in the vertical.

2. The vertical component is constant g = 9.8 m/s2.

3. The vertical to horizontal motion changes according to that of

the greater force.

Anatomy of projectile motion.

Kinematic Equations:

EquationSituation 1: Object initially travels in

the horizontal with vy = 0

x = vx∆t :displacement in the horizontal as a function of time.

y = vyi∆t + 1/2g∆t2 :displacement in the vertical as a function of time.

Final velocity horizontal is: Vxf = Vi

Final velocity vertical is : Vyf = g∆t

NOTE: For situation 1.1. horizontal acceleration in constant with a change in position.2. vi horizontal = vf horizontal

3. Objects in trajectory will fall at the same rate whether dropped or in trajectory.

Solution:1. List all of the known and unknown components as well as the constants. 2. Write the equations that best defines the question base on the list you just made.3. Match variables to equation and solve.

Sampler

1. A ball rolls off a table top at 3.2 m/s. If the table is 0.97 m high, how many seconds will it take for the ball to hit the floor? What is the range?

Sampler

2. What is the range of a rock thrown from a 84 m building with a horizontal velocity of 5.2 m/s?

Sampler

3. An object is thrown horizontally over a cliff at a speed of 5 m/s. The height of the cliff is 78.4 m.

a. How long does it take for the object to reach the bottom of the cliff?

b. How far from the base of the cliff does the object strike the ground?

c. What is the horizontal and vertical component of the velocity of the object just before it hits the ground?

Sampler

4. A steel ball rolls with a constant velocity across a table top 0.95 m above the floor. It rolls off the table top and hits the floor 0.352 m horizontally from the edge of the table top. How fast was the steel ball rolling?

Sampler

A ball rolls off a table top at 3.2 m/s. If the table height is 0.97 m, how many seconds will it take for the ball to hit the floor? What is the range?

LEQ

What are the variables that define the motion of a soccer ball when it is kicked?

Anatomy of Trajectory:

y = zero ; displacement in the y direction is zero.

x = range ; velocity in the x-axis times flight time.

Time of flight is found by: y = vy t + 1/2g t2

Maximum height of flight is y at half the time, t .

NOTE: Situation #2. When y = 0Trends:

1. vx = vinitialcosѲ and vy = vinitialsinѲ

2. displacement in the vertical is zero. y = 03. time up = time down4. vertical displacement is found for ½ the flight time.5. 45o optimal trajectory but 30o and 60o compliment each other as equal and opposite.6. low trajectory mean low flight time.7. gravity is -9.8 m/s2

Equations for Situation #2Horizontal displacement (how far)

x = vx∆t

Timey = Vy∆t + 1/2g∆t2 w/ y =

oVertical displacement (how high)

y = vy∆t + 1/2g∆t2 w/ t = 1/2t

Situation #2 SamplersA mouse soccer ball is kicked (by a

mouse) at an angle of 66o from the horizontal at an initial velocity of 4.5 m/s.

a. How long does the ball take to land?b. How high will the ball travel?c. What is the total distance traveled>

Range?

Situation #2 Sampler

2. A cannonball is fired at an angle of 30o to the horizontal at a speed of 49.2 m/s.a. What is the total time of flight for the cannonball?b. How high will the cannonball travel?c. How far will the cannonball travel >Range?

Questions:

LEQ

What variables affect the motion of an object along a circular path?

Pendulum Period is the time for one swing. (up

and back)

T = 2π length/ l g l

2 pie time square root of length of the pendulum divided by the absolute value of gravity.length refers to the length of the pendulum.

Circular Motion/Gravity

Velocity in a circular path: the speed a body moves is a ‘period’ is:

v = 2πr / Tr = radius of the circular pathT = period = the time for one revolutionAs the radius decreases, the period also decreases and the velocity most increase.

Centripetal Force

The force that acts toward the center of that circular path.

Fc = mac

Where ac, centripetal acceleration, is the rate change in speed as the body moves toward the center of a circular path.

ac = v2 / r

Sampler 1 A 53 Kg cart takes 2.3 s to travel around a circular path at a uniform speed. The path has a diameter of 4.8 m.a) What is the centripetal acceleration of the cart?

ans: 17.9 m/s2b) What is the centripetal force?

ans: 949.3 N

Sampler 2In the hammer throw, an athlete whirls a 7 Kg hammer tied to a 1.3 m long cable. If the athlete whirls at a rate of 1 rev/s:a) What is the centripetal acceleration?

ans: 51.3 m/s2

b) What is the force exerted on the chain or tension?

ans: 359.3 N

Sample 3

A pendulum has a length of 1.3 m.a) What is the period?

ans: 2.29 sb) To halve the period, what is the length of the pendulum?

ans: 0.33 mc) What is the length of the pendulum if the original period doubles?

ans: 5.2 m

Circular Motion/Gravity

Velocity in a circular path: the speed a body moves in a ‘period’. (v)Period: (T) the time for one revolution

v = 2πr / TCentripetal force: the force that acts on a

body toward the center of a circular path.Fc = mac

Centripetal acceleration: the acceleration of a body toward the center of a circular path.

ac = v2 / r