PHYS16  Lecture 6

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PHYS16 – Lecture 6. Physics of 2D Motion September 20, 2010. To run or walk???. Agenda. Administration Key Concepts – Physics 2D motion Relative Motion. Administration. Homework Assignments Due Tuesday, Online lab homework Due Sunday, Written homework, &amp; Ch. 4 Online homework

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### PHYS16 – Lecture 6

Physics of 2D Motion

September 20, 2010

To run or walk???

Agenda
• Key Concepts – Physics 2D motion
• Relative Motion
• Homework Assignments
• Due Tuesday, Online lab homework
• Due Sunday, Written homework, & Ch. 4 Online homework
• Help Sessions – T/TH 8-9pm
• View Jupiter – Tonight 9 pm, Merrill Beach
Review Questions
• Let’s say you have a velocity vector that is 6 mph at 55 degrees relative to the x axis. What is the component of the vector along x?
• A) 6cos(55 degrees)
• B) 6sin(55 degrees)
• C) 6/sin(55 degrees)
• D) 6tan(55 degrees)

6 mph

?

Review Questions
• If you add vector 1 (5 at 37 degrees) to vector 2 (2 at 0 degrees), what do you get for the component in the x direction?
• A) 5
• B) 4
• C) 6
• D) 7
Review Questions
• v=at+v0 , what does x=?
• x=(1/2)at2+v0t+x0
Review Questions
• When you throw a ball up, at max height, acceleration in y is? (-9.8 m/s2)
• When you throw a ball up, at max height, velocity in y is? (0 m/s)
• A car goes from 0 to 4 m/s in 0.5 s. What is the car’s acceleration? (8 m/s2)
Usain Bolt vs. a Fly

Usain’s Position vs. time

Except between time

0 s to 1.89 s, Usain has a

constant velocity of ~10 m/s

Usain’s acceleration = 0 m/s^2

Usain Bolt vs. Fly

Position vs. time for two flies

Each dot is a position at 20 Hz

Velocity vs. time and acceleration vs. time is more complicated than Usain Bolt

Key Concepts: Physics 2D Motion
• 2D Motion
• Independent in x and y
• Constant acceleration
• Relative Motion
• Projectile Motion
2D Motion
• Motion in x and motion in y is independent
• Separate into motion in x and motion in y
• Use the equations of motion for 2D to solve for unknowns
• Separate and Solve
• Most problems will assume constant acceleration
• Equations of motion?
Relative Motion – Math
• Relative motion – motion of a frame that an object is moving in
• Motion of object in frame is just equal to object’s motion
• Motion of object out of frame is equal to object’s motion + frame motion
Relative Motion – Walkway at Airport
• I am running at 2 m/s in the airport and the moving walkway is at 3 m/s. If I take the walkway what is my speed?
• 5 m/s
• Do I take the walkway or run if there is a family on walkway so that I can’t run on it?
• take walkway
• If I just run the 10 m to the gate instead of taking the walkway will I still beat my brother who is going 3 m/s and is 11 m behind me?
• yes
Relative Motion – River Problem
• A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value?

4 m/s

3 m/s

Relative Motion – River Problem
• A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value?
• 5 m/s at an angle of 40 degrees from the shore
Relative Motion – Bucket Problem
• A bucket is left out in the rain. The rain is coming down at 5 m/s. If a crosswind starts to blow at 2 m/s, will the bucket fill faster or slower?

Wind at

2 m/s

Original rain

5 m/s

5 m/s

Scenario #2

Scenario #1

Relative Motion – Run or Walk in Rain?
• Is it better to run or walk in the rain?
Relative Motion – Run or Walk in Rain?
• Is it better to run or walk in the rain?
• Assume rain is coming straight down at 1 m/s
• If you run at 2 m/s, what does the rain look like in your frame?
• looks like coming at you instead of straight down
• If you just look at surface area of body getting wet, does walking or running hit less surface area?
• Walking
• If you look at how many rain drops hit you, does walking or running have less total rain drops?
• Running because you reach your destination sooner
Summary
• Separate 2D motion into x and y and then solve
• Use Kinematic equations of Motion to solve for problems with constant acceleration
• Relative Motion – make sure to add velocity of frame to velocity of object to get relative velocity