AP Physics C
Aim: How do I find the acceleration vector? Describing Motion in 2-D Intro Lesson
AP Physics C: 2-D Kinematics
Do Now:
1. At time t=0 a ball of mass m is thrown vertically from a point P (x=0, y=0) with an initial velocity of vxi +vyj.
a. Express the velocity vector v(t) of the ball at time t using the given information and the constant g.
b. Give an expression for the position vector r(t) of the ball relative to the point P at time t.
Question: When do you get an acceleration? Look at the two diagrams below that describe average acceleration and instantaneous acceleration.
[pic] [pic]
Describing Acceleration:
[pic] [pic]
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PRACTICE: Interpret this Motion Diagram- Describe in words and draw in acceleration vector
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Trajectory in x-y plane
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DIFFERENCE BETWEEN s-t plot and trajectory plot [pic]
If acceleration is constant, then NO NEED TO USE CALCULUS
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Example Problem 1:
The thrusters on the shuttlecraft starship Enterprise geives it an pward acceleration of 5.0 m/s2. Its forward thrusters give it an accleration of 20 m/s2. As it leaves the Enterprise, the shuttle turns on only the up thrusters. After clearing the flight deck, 3.0 seconds later, it adds the forward thrusters. Plot the shuttle’s trajectory.
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Aim: How can I use vector understanding to solve projectile motion problems?
Do Now: Projectile motion workbook questions
Brief Review of PJM
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EXAMPLE PROBLEM 2:
A baseball is hit at an angle θ and is caught at the height from which it was hit. If the ball is hit at a 30.0 degree angle, with what speed must it leave the bat to travel 100 m? Use 10 m/s2 for g and assume no air resistance.
Discussion Problems:
Problem4- 11 A Physics student on planet Exidor throws a ball, and it follows the parabolic trajectory shown below with the information of the instantaneous velocity given for t=1s.
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a. Determine the ball’s velocity at t=0 s, 2s, and 3s?
b. What is the value of g on planet Exidor?
c. What was the ball’s launch angle?
Learning Assessment: Do this problem on a separate sheet and submit
A flying saucer maneuvering with constant acceleration is observed with the positions and velocities show below. What is the saucer’s acceleration a (magntidue and direction)?
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Hit the box problem
Students at an engineering contest use a compressed-air cannon to shoot a softball at a box being hoiseted straight up at 10 m/s. The cannon tilted upward at an angle of 30 degrees, is 100m from the box and fires by remote control the instant the box leaves the ground. Students can control the launch speed of the softball by setting the air pressure. What launch speed shuod the students use to hit the box?
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WARM-UP: An object moves in a ccw direction in a circular path at constant speed, the object’s acceleration can best be described as (Choose what fits and why)
1. Zero, since there is it is moving at a constant speed
2. Constant in magnitude but nonzero and Directed tangentially
3. Constant in magnitude but nonzero and Directed inwards
4. Constant in magnitude but nonzero and Directed outwards
5. None of these
Uniform Circular Motion
Uniform Circular Motion:
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Angular Position, θ:
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Period, Τ:
Angular Displacement Δθ:
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Angular velocity, ω
Sign Conventions
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Velocity and Acceleration for UCM
[pic][pic]
Tangential Velocity:
Centripetal Acceleration:
Tangential Velocity and Centripetal Acceleration’s relationship to Angular Velocity:
Learning Check: Rank in order, from largest to smallest, the centripetal accelerations (ar)a to (ar)e of particles a to e.
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Nonuniform Circular Motion
Tangential Acceleration
Radial Acceleration
Net Acceleration
[pic] [pic]
Note: If at is constant, you can use the constant acceleration equations to find arc length, s, and tangential velocity, vt PUT EQUATIONS HERE
Angular Acceleration, α
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Note: Two points on a rotating object have the same angular acceleration, but in general have different tangetial accelerations because they are moving in circles of different radii.
For constant angular accleration in non-uniform circular motion, you can use the rotational kinematic form of our old best friends:
You Have Four Possibilities (careful on what the sign of each means)
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SAME OLD THING WITH GRAPHS!
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How can this happen? Give a real example
˜8™8š8?8¹8÷8ø8ú8û8ý8þ89[pic]999!9"9#9L9M9^>„>†>ˆ>Š>÷÷òòêåÛÙÛÙÛÙÛÙÔSAME OLD THING WITH HOW θ, ω,and α ARE RELATED
PUT EQUATIONS HERE
Motion Plots for angular motion are just like the linear ones as well!
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