physics 151: lecture 5, pg 1 announcements: l physics learning resource center open, –> room...

Physics 151: Lecture 5, Pg 1

Announcements:Announcements: Physics Learning Resource Center Open,

– > room P207-COpen 9am - 5 pm Monday - FridayHours also listed on www.phys.uconn.edu

NOTE:

Homework #1 (due this Fri. 9/8 by 5:00 pm EST on WebAssign)

Homework #2 (due next Fri. 9/15 by 5.00 pm)


Projectile motion

Uniform circular motion

text sections 4.1-4.5

Physics 151: Lecture 5Physics 151: Lecture 5Today’s AgendaToday’s Agenda

(Chapter #4)(Chapter #4)


ACT -1ACT -1Question from past Exam-1Question from past Exam-1

Which statement is true.

1. Initial speed of ball B must be greater than that of ball A.

2. Ball A is in the air for a longer time than ball B.

3. Ball B is in the air for a longer time than ball A.

4. Ball B has a greater acceleration than ball A.

5. None of above.

Two balls, projected at different times so they don’t collide, have trajectories A and B, as shown.


Review : Kinematics in 3D (2D)Review : Kinematics in 3D (2D) Motion of objects in 3-D under constant acceleration

(problem in projectile motion) :

y

x

-> independence of x- and y- components :

yy (t)(t)

xx (t)(t)

aayy= -g= -g

aaxx=0=0

yyoo

xxoo

ttoo= 0= 0

ttvx

vy

vvoovoy

vox

y = y0 + v0y t - 1/ 2 g t2

vy = v0y - g t

x = vx tvx = v0x

x-components (a=0)

y-components (a=-g)

Animation (v) Animation (a)


Review : Kinematics in 3D (2D) (cont.)Review : Kinematics in 3D (2D) (cont.)

y

x

yy (t)(t)

xx (t)(t)

aayy= -g= -g

aaxx=0=0

yyoo

xxoo

ttoo= 0= 0

ttvx

vy

vvoovoy

vox

How many parameter determine projectile motion ?

at to = 0: xo, yo , vox, voy

at t = t : x(t) , y(t), vx, vy

9 variablesplus a=g {

we have 4 equations !

}4 independent variables !


Projectile MotionProjectile Motion

Typical Questions,1. x: How far will it go ?

2. y: How high will it be at some distance ?

3. t: How long until it hits ?

4. : At what angle should I start ?

5. v0: How fast must I start ?

v0

g


Projectile MotionProjectile Motion

Useful Things to Know

If projectile begins and ends at same height, maximum distance is achieved for = 45°. (prove it)

x distance is same for angles about 45° if everything else remains the same.

Time in flight depends on y equation if no barriers other than the earth interrupt the flight path.

v0

g


Projectile Motion / Example ProblemProjectile Motion / Example Problem

v0

g

UConn football team wants to complete a 45m pass (about 50 yards). Our qb can throw the ball at 30 m/s.

At what angle must he throw the ball to get it there ?

SOLUTION: = 15° or 75° which gets there first ?


Problem 3Problem 3 (correlated motion of 2 objects in 3-D) (correlated motion of 2 objects in 3-D)

Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground.

t = t1

y

x

vv00

t = 0

t = 0TARGET

PROJECTILE

( A ) MISS ( B ) HIT ( C ) CAN’T TELL

Would the projectile now miss or hit the target ?


ReviewReview( displacement, velocity, acceleration )( displacement, velocity, acceleration )

Velocity :

Acceleration :

a = dvv / dt

3-D Kinematics : vector equations:

rr = rr(t) vv = drr / dt aa = d2rr / dt2

v = drr / dt

vav = rr / t

aav = vv / t

vv2

vv-v-v1

vv2

y

x

path

vv1


General 3-D motion with non-zero acceleration:General 3-D motion with non-zero acceleration:

Uniform Circular Motion is one specific case of this :

aa

vpath

t

aa

aa

aa = 0

because either or both:

-> change in magnitude of v

-> change in direction of v

aa = 0

aa = 0

aaaaaa= +

Animation


Uniform Circular MotionUniform Circular Motion

What does it mean ?

How do we describe it ?

What can we learn about it ?

See text: 4-4


What is Uniform Circular Motion (UCM) ?What is Uniform Circular Motion (UCM) ?

Motion in a circle with:

Constant Radius R

Constant Speed v = |vv|

acceleration ?

R

vv

x

y

(x,y)

See text: 4-4

= 0aa

aa

= const.aa


How can we describe UCM?How can we describe UCM?

In general, one coordinate system is as good as any other: Cartesian:

» (x,y) [position]» (vx ,vy) [velocity]

Polar:» (R,) [position]» (vR ,) [velocity]

In UCM: R is constant (hence vR = 0). (angular velocity) is constant. Polar coordinates are a natural way to describe UCM!Polar coordinates are a natural way to describe UCM!

RR

vv

x

y

(x,y)

See text: 4-4


Polar Coordinates:Polar Coordinates:

The arc length s (distance along the circumference) is related to the angle in a simple way: s = R, where is the angular displacement. units of are called radians.

For one complete revolution:

2R = Rc

c = 2

has period 2.RR

vv

x

y

(x,y)s

See text: 4-4

1 revolution = 21 revolution = 2radiansradians


Polar Coordinates...Polar Coordinates...

In Cartesian co-ordinates we say velocity dx/dt = v. x = vt

In polar coordinates, angular velocity d/dt = . = t has units of radians/second.

Displacement s = vt.

but s = R = Rt, so:RR

vv

x

y

st

v = R


Period and FrequencyPeriod and Frequency Recall that 1 revolution = 2 radians

frequency (f) = revolutions / second (a)angular velocity () = radians / second (b)

By combining (a) and (b) = 2 f

Realize that:period (T) = seconds / revolutionSo T = 1 / f = 2/

RR

vv

s

= 2 / T = 2f

vv

R

s


Lecture 5, Lecture 5, ACT 2ACT 2Uniform Circular MotionUniform Circular Motion

A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ?


Acceleration in UCM:Acceleration in UCM:

This is called This is called Centripetal Acceleration. Now let’s calculate the magnitude:

vv1vv2

vv

vv2

vv1RR

RR

vv

RR

Similar triangles:

But R = vt for small t

So: vv

v tR

vt

vR

2

avR

2


Lecture 5, Lecture 5, ACT 2ACT 2Uniform Circular MotionUniform Circular Motion

A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ?

(a) 20 m(b) 200 m(c) 2000 m(d) 20,000 m


Recap for today:Recap for today: Recap of Projectile Motion

Introduce Uniform Circular Motion

Reading assignment for MondayReread Circular Motion: Ch 4.4-4, pp.91-95Read Relative Velocity: Ch 4.5, pp.95-99

Homework #1 (due this Fri. 9/8 by 5:00 pm EST on WebAssign) Problems from Chapter 1 and 2

Homework #2 (due next Fri. 9/15 by 5.00 pm)Problems from Chapter 3 and 4

physics 151: lecture 5, pg 1 announcements: l physics learning resource center open, –> room...

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