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King Fahd University ofPetroleum & Minerals

Mechanical Engineering

Dynamics ME 201

BY

Dr. Meyassar N. Al-HaddadLecture # 14

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Projectile Determine the speed at which

the basketball at A must be

thrown at the angle of 30oso

that it makes it to the basket at

B. At what speed does it pass

through the hoop?

tss

Horizontal

oo

toA 30cos010

2

2

1tatss

Vertical

coo

2)81.9(2

130sin5.13 ttoA

933.0tsmA /4.12

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A ball traveling at 25 m/s drive off of the edgeof a cliff 50 m high. Where do they land?

25 m/s

Vertically

v = v0-gt

y = y0+ v0t + 1/2gt2.

v2= v02- 2g(y-y0).

Horizontally

x = x0 + (v0)x t x = 25 *3.19 = 79.8 m

79.8 m

Initial Conditions

vx= 25m/s

vy0= 0m/s

a =- 9.8 m/s

2

t = 0

y0= 0 m

y =- 50 m

x0=0 m

V2= -2(9.8

)(-50-0)V = 31.3 m/s

-50 = 0+0+1/2(-9.8)t2 t = 3.19 s

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Example 13-4

m A= 3 kg

m B= 5 kg

From rest

vB= ? In 2 second

yy maF AaT 32981

Block A

yy maF BaT 52.196

Block B

lss BA 2 02 BA 02 BA aa

taBo

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VA= ?

2Sc+ S

A= L

2ac+ aA= 0

aA= -2ac

ca

ccx

y

amgTNmaF

NNNF

20030sin25.0:

1699030cos81.9*200:0

Problem

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Relative motion At the instant shown, cars A and

B are traveling at the speeds

shown. If B is accelerating at

1200 km/h2while A maintains a

constant speed, determine the

velocity and acceleration of Awith respect to B.

BABA /vvv

BA

oo

/vi65j45sin20i45cos20

j14.14i14.79v / BA

hkmBA /4.80)14.14()14.79(v 22

/ BABA /aaa

BA

oo

/

22

ai1200j45sin1.0

)20(i45cos

1.0

)20(

j2828i1628a / BA

222

/ /3260)2828()1628( hkma BA

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Polar and Cylindrical The slotted fork is rotating about O at a

constant rate of 3 rad/s. Determine the radial

and transverse components of velocity and

acceleration of the pin A at the instant q= 360o.

The path is defined by the spiral groove r =(5+q/p)in., where qis in radians.

pq

pq p

q

p

q

rrr 752

032360

qqpq

o

sinrvr /955.03

p

sinrv /21)3(7 qq

222 /63)3(70 sinrrar q

2/73.5)3)(3(202 sinrra p

qqq

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Example 12-20

qq

q

q

andfind

180atft/s30

ft/s4

ft)cos1(5.0

o2

a

v

r

)cos1(5.0 qr

qq )sin(5.0rqqqqq )sin(5.0)()(cos5.0 r

2

o

500ft1

180at

.-rrr

q

rad/s44)1()0()()( 2222 qqq rr

30)]4)(0(21[])4(1)4(5.0[)2()( 2222222 qqqq rrrra

2rad/s18q

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Problem 13-89Smooth

Horizontal

m = 0.5 kg

r = (0.5 q)

q = 0.5 t2rad

Applied force

Normal force

t = 2 s.

q

r

qqq

5.05.05.0 rrr15.0 2 qqq tt

2

2

/5.0/11

/1/26.1142

sec2

smrsmrmr

sradsradrad

tat

o

qqq

o

radddr

r

43.63

5.0

5.0

/tan

2

q

q

q

222 /5.3)2(15.0 sftrrar q2/5)2)(1(2)1(12 sftrra qqq

NFFmaF

NNNmaF ccrr

62.1)5(5.043.63cos96.1

96.1)5.3(5.043.63sin

qq

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Problem

m=2 kg

Smooth horizontal

r = 0.4 qPtangent=?

N=?

At q = 45o

qqq 4.04.04.0 rrr

0/64

45 qqp

q srado

0/4.21.0 rsmrr p

222

/31.11)6()1.0(0 smrrar pq

2/8.28)6)(4.2(202 smrra qqq

o

ddr

r15.38

44.0

4.0

/tan

pq

q

q

)31.11(215.38sin15.38cos; NPmaF rr )8.28(215.38cos15.38cos; NPmaF qq

NPNN 8.173.59

PN

r

q

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