Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture...

14
Mi it ftd ’l t Physic 231 Lecture 4 Main points of todays lecture: Example: addition of velocities Trajectories of objects in 2 dimensions: dimensions: 2 downwards m/s 9.8 g = ( ) t v v y y y gt v v yo y y y 0 0 2 1 + = Δ = y g v v gt t v y y y y 2 0 2 2 0 2 2 1 Δ = = Δ t v x v v x x x 0 0 = Δ =

Transcript of Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture...

Page 1: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

M i i t f t d ’ l t

Physic 231 Lecture 4

• Main points of today’s lecture:• Example: addition of velocities• Trajectories of objects in 2

dimensions:dimensions:

2 downwards m/s 9.8 g =

( )tvvyyy

gtvv

yoy

yy

0

0

21 +=−≡Δ

−=

ygvv

gttvy

y

y

y2

02

20

221

Δ−=−

−=Δ

tvxvv

x

xx

0

0

=Δ=

Page 2: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Example:

A f tb ll l th tt i i th d i b th th• A football player runs the pattern given in the drawing by the three displacement vectors A, B and C. The magnitudes of these vectors are A=5 m, B=15 m, and C=18 m. Using the component method, find the magnitude and direction of the resultant vector A+B+Cmagnitude and direction of the resultant vector A+B+C.

label x-comp y-compA 0 5 mB 15 m 0C 14.7 -10.3mR 29 7 5 3R 29.7m -5.3,m

0x

0

C 18m cos(35 ) 14.7m;

C 18msin(35 ) 10.3m;

= =

= = −R=

yC 18msin(35 ) 10.3m;

2 2R 29.7 5.3 30.2mtan( ) 5 3 / 29 7θ

= + == −

0

tan( ) 5.3 / 29.710.1

θθ = −

Page 3: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

quiz

B b t l 3 k d t d th t l 4 k d th R l ti t• Bob travels 3 km due east and then travels 4 km due north. Relative to his starting position what is the magnitude of his total displacement and the angle with respect to due east?

) 7 k 35 d t th th f d t– a) 7 km, 35 degrees to the south of due east.– b) 7 km, 53 degrees to the north of due east– c) 5 km, 35 degrees to the south of due east– d) 5 km, 53 degrees to the north of due east

vector x comp. y comp.

BR

A 3 km 0

B 0 4 km

3 k 4 k

A

R 3 km 4 km

543 2222yx kmRRR =+=+=

east due of north ,53333.1tan o

x

y

RR

===θ

Page 4: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

relative velocity problems

L b l h bj t b l tt th t i d f h t it i (f• Label each object by a letter that reminds you of what it is (for example p for paper, g for ground, t for truck).

• Look for phases such as "the velocity of the paper relative to truck" d it th l itand write the velocity as:

pttrucktorelativepaper vv =___

• Take the three velocities and assemble them into an equation such as;pttgpg vvv +=

• Take the three velocities and assemble them into an equation such as;

S l f th l it t N t th t th l iti d t b• Solve for the velocity you want. Note that these velocities need not be parallel. You may need to solve two equations, one in the x direction and another in the y direction.

Page 5: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

exercise

Ch k l k h d d G d H H th hi• Chuck looks ahead and sees Grandpa Harper. He throws him a newspaper over the top of the hood to him. The truck is moving 40 km/hr due West. Relative to the truck, the newspaper also moves West with a velocity of 40 km/hr What is the velocity of the newspaperwith a velocity of 40 km/hr. What is the velocity of the newspaper relative to Grandpa Harper? – a) 0 km/hr

b) 80 k /h d t groundtorelativepaperv– b) 80 km/hr due west– c) 80 km/hr due east– d) don’t know 4040

___

___

+=

+=

groundtorelativepaper

trucktorelativepapertruck

groundtorelativepaper

vvv

Westkm/hr 80___

=gp p

vtruck 40 km/hr West

vpaper relative to truck 40 km/hr West

vpaper relative to ground ?

Page 6: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Example

A f b t i t li i di ti 35 1o th f t ith d• A ferry boat is traveling in a direction 35.1o north of east with a speed of 5.12 m/s relative to the water. A passenger is walking with a velocity of 2.71 m/s due east relative to the boat. What is the velocity (magnitude and direction) of the passenger with respect to the water?no

rth

(magnitude and direction) of the passenger with respect to the water?

eastx

y

n

pw pb bwv v v= +

bw xv 5.12cos(35.1 ) 4.19m / s= ° =

vpb= 2.71 m/s

east bw,x ( )

bw,yv 5.12sin(35.1 ) 2.94m / s= ° =

x y mag θ

vpb 2.71 0 2.71 0

vbw 4.19 2.94 5.12 35.1°

v 6 9 2 94 7 5 23°

35.1oθ

vpw 6.9 2.94 7.5 23°

2 2pwv 6.9 2.94 7.5m / s= + =

( )1 2 94vpb= 2.71 m/s ( )1 2.94tan 23 north of east6.9θ −= = °

Page 7: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Projectile motion in two dimensionsgtvtavv yyyy −=+= 00 00 =+= vtavv xxxx

( )

gttvtatvy

tvvyyy yoy

−=+=Δ

+=−≡Δ

1121

22

0 ( )1

21

2

00

=+=Δ

=+=−≡Δ

tvtatvx

tvtvvxxx xxox

ygyavv

gttvtatvy

yy

yyy

y Δ−=Δ=−

=+=Δ

2222

20

2

00

022

20

2

00

=Δ=−

=+=Δ

xavv

tvtatvx

xx

xxx

x

hi h h f h l i i h• This means that the x-component of the velocity remains constant. The y-component reflects the gravitational acceleration.– This is true; contrary to the presentation of Jason below:

Page 8: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Projectile MotionThe horizontal motion isThe horizontal motion is constant; the vertical motion is free fall:

The horizontal and vertical components of the motion are independent.

Slide 3-37

Page 9: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

example

A b ll t i fi d f ifl th t i h ld 1 6 b th d i• A bullet is fired from a rifle that is held 1.6 m above the ground in a horizontal position. The initial speed of the bullet is 1100 m/s. Find (a) the time it takes for the bullet to strike the ground and (b) the horizontal distance traveled by the bullethorizontal distance traveled by the bullet.

If upward is the direction of positive y:

vx0 1100 m/s

vy0 0

direction of positive y:

Δy -1.6 m

Page 10: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

clicker question• The diagram below shows two

successive positions of a particle; it'ssuccessive positions of a particle; it's a segment of a full motion diagram. Which of the following vectors best represents the acceleration betweenrepresents the acceleration between

)

i fv and v

a)

b)

c)

d)d)

Page 11: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

example

A ll i h i f th ili A ifl i i d di tl t th• A small can is hanging from the ceiling. A rifle is aimed directly at the can, as the figure illustrates. At the instant the gun if fired, the can is released. Ignore air resistance and show that the bullet will always strike the can regardless of the initial speed of the bullet Assume thatstrike the can, regardless of the initial speed of the bullet. Assume that the bullet strikes the can before the can reaches the ground.

Δygravity Δycan

θ

Page 12: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Reading Quiz 2. The acceleration vector of a particle in projectile motion2. The acceleration vector of a particle in projectile motion

A. points along the path of the particle.B. is directed horizontally.C i h t th ti l ’ hi h t i tC. vanishes at the particle’s highest point.D. is directed down at all times.E. is zero.

Slide 3-9

Page 13: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

example• A motorcycle daredevil is attempting to jump across as many buses asA motorcycle daredevil is attempting to jump across as many buses as

possible (see the drawing). The takeoff ramp makes an angle of 18.0°above the horizontal, and the landing ramp is identical to the takeofframp. The buses are parked side by side, and each bus is 2.74 m wide.p p y ,The cyclist leaves the ramp with a speed of 33.5 m/s. What is themaximum number of buses over which the cyclist can jump?

33 5 m/s33.5 m/s _ _

2.74m

v0 33.5 m/s gtvv yy −= a) 0y0v 33.5sin(18 ) 10.35m / s= ° =

21

θ 18o ( )

gttvy

tvvyyy yoy

−=Δ

+=−≡Δ

1c)

21 b)

20

0

2y0

1y v t gt 02

Δ = − =

2y0

1v t gt2

= y02vt 2.11s

g

Which equation to use?ygvv

gttvy

y

y

y Δ−=−

Δ

2 d)2

c)

20

2

0x0x v t 33.5cos(18 )(2.11s) 67.25mΔ = = ° =

busesbus

x 67.25mN 24.5 24busesw 2.74mΔ= = =

Page 14: Physic 231 Lecture 4 - Directory | National ...lynch/phy231_2010/lecture4.pdf · Physic 231 Lecture 4 ... Concept problem • A battleship simultaneously fires two shells at enemy

Concept problem• A battleship simultaneously fires two shells at enemy ships. If

the shells follow the parabolic trajectories shown which shipthe shells follow the parabolic trajectories shown, which ship gets hit first?

– a) Ab) both at the same time :Bfor velocity verticalinitialthe

exceedsA for velocity verticalinitial

– b) both at the same time– c). B– d) need more information

ByAyA

topy

vvhhghv

ghvv

,0,020

20

2,

;2

02y

>>=

=−=

B

ytottottotytot

yy

gv

tgttvy 020

,,

2210 =−==Δ

BtotAtotByAy ttvv ,,,0,0

:iestrajectortwothecomparing>>