PHYS16 – Lecture 6

Physics of 2D Motion September 20, 2010

To run or walk???

• Administration• Key Concepts – Physics 2D motion• Relative Motion

Agenda

• 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

Administration

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

Except between time 0 s to 1.89 s, Usain has aconstant velocity of ~10 m/s

Usain’s acceleration = 0 m/s^2

Usain’s Position vs. time

Usain Bolt vs. Fly

Position vs. time for two fliesEach 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

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?

Kinematic Equations

)(2 III.

2 II.

I.

020

2

200

0

xxavv

ta

tvxx

tavv

xxx

xx

xxx

)(2 III.

2 II.

I.

020

2

200

0

yyavv

ta

tvyy

tavv

yyy

yy

yyy

X Y

Relative 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

frameobjectrelative vvv

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?

5 m/s Original rain5 m/s

Wind at2 m/s

Scenario #1 Scenario #2

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