Society of Young Engineers Towards Achieving Excellence

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BASPHYS Quiz 1

8i + 5 j − 7k
8i − 5 j − 7k
8i − 5 j − k
8i + 5i − k

R
1
B 6

A 6
6
A+ B + R = 0 1
A + B = −R 6
A+ B = R 36
−( A + B ) = R

m
6
s
m
6
s
m
6
s

a = 3i + 2 j + 2k b = 2i − j + 3k

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BASPHYS Quiz 1

1.16m
1.30m

5500N
m a 5
4.0
s2 53.13
b = 5i − 12 j
m
g = 10 a
s2 3a + (2b − a)
1600N
a•b
3300N
4400N
7700N m
3.5
F m s
a m
200m 1.7
5m s

5a
25a
a
5
a
25
750m

8.5s
2.0844 10−7 N
60kg 8.5s
75kg

−11 m3
G = 6.67  10
kg s 2
1.20m
1.23m

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BASPHYS Quiz 1

m
20
s T2
25 T1

7.5kg
19

0.25

0.6kg
T1 T2

60 30

60 30

T1 T2

0.6kg

m
g = −10
s2

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BASPHYS Quiz 1

i j k
ab 3 2 2
2 −1 3

2 2 3 2 3 2
=i −j +k
−1 3 2 3 2 −1
A B = i[(2)(3) − (−1)(3)] − j[(3)(3) − (2)(2)] +
k[(3)(−1) − (2)(2)]
B = i (6 + 2) − j (9 − 4) + k (−3 − 4)
A a  b = 8i − 5 j − 7k

v 2 sin 2  1
A B R H= gM = g
2g 6
v 2 sin 2  v 2 sin 2  3v 2 sin 2 
R B HM = = =
2gM 1 g
A 2( g )
6
x=
H M = xH
3v 2 sin 2  v 2 sin 2 
= ( x)
g 2g
A+ B + R = 0 3 v 2 sin 2  2g
( 2 2 )=x
g v sin 
H M = 6H

a = 3i + 2 j + 2k
b = 2i − j + 3k

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BASPHYS Quiz 1

W = mg  5500 = m(10) a=5

 m = 550kg
ax ay
 F = ma (5cos53.13 )i (5sin 53.13 ) j
 T − mg = ma
 T = (550)(10) + (550)(4) 53.13 a = 3.00i + 4.00 j
 T = 7700 N

3a + (2b − a)
Gm1m2
Fg = 3(3.00i + 4.00 j ) + [2(5i − 12 j ) − (3.00i + 4.00 j )]
r2
9i + 12 j + (10i − 24 j − 3i − 4 j )
−11 m3
(6.67  10 )(60kg )(75kg ) 9i + 12 j + (7i − 28 j )
−7 kg s 2
2.0844  10 N = 9i + 7i + 12 j − 28 j
r2
m3 16i − 16 j
(6.67  10−11 )(60kg )(75kg )
kg  s 2
r2 = a b = ax bx + a y b y
m
2.0844  10−7 kg  2
s a b = (3  5) + [4  (−12)]
−11 m32 a b = 15 − 48
(6.67  10 )(60 kg )(75 kg )( s 2 )
kg  s 2

r2 = a b = −33
2.0844  10−7 kg  m
(6.67  10−11 m 2 )(60)(75)
r=
2.0844  10−7
a b =| a || b | cos 
a=5
ab
r = 1.20m 2 2 = cos
b= b +b x | a || b |
y

b = 52 + (−12) 2 −33 = cos

| 5 ||13 |
b = 25 + 144
−33
a b = 169 cos −1 ( ) =
65
b = 13  = 120.51

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BASPHYS Quiz 1

vbr = 3.5m / s vrs = 1.7m / s d = 200m

vrs d 1.7 d
=  =
vbr 200 3.5 200
 d = 97.1429  97.14m

m
vbs v0 = 0; a = −9.8 ; h = 750m
s2
0
vbs = (vbr ) 2 + (vrs ) 2 750m
 vbs = 3.5 + 1.72 2

m
 vbs = 3.8910  3.89
s
8.5s

 m 
x = vbr t v f = v0 + at = 0 +  −9.8 2  (8.5 s )
 200 = (3.5)t  s 
 t = 57.1429  57.14sec m
v f = −83.3
s

8.5s

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BASPHYS Quiz 1

1 1 m
d yf = d y 0 + v0t + at 2 = 0 + 0 +  −9.8 2  (8.52 s 2 )
2 2 s 
 m
v 2f = v02 + 2a  d y = 0 + 2  −9.8 2  (−750m)
 s 
d yf = −354.025 dis tan cey = 354.025m
m2 m
v = −9.8(−750) 2
2
f v f = −121.24
s s

8.5s
m
vo = 20  = 25
h8.5 s = h − dis tan cey = 750m − 354.025m s
h8.5 s = 395.975m

1
y = − gt 2 + (vo sin  )t
2

t
t
1
d fy = d y 0 + v0t + at 2
2
1 m
−750m = 0 + 0 +  −9.8 2  t 2 0m / s
2 s 
v y = − gt + vo sin 
−750 m s 2
 0 = −(9.81)(t ) + (20)(sin 25 )
= t2 t = 12.3718s
−4.9 m  t = 0.862sec

750m
d fy

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BASPHYS Quiz 1

1 x = (vo cos )t
y = − gt 2 + vo (sin  )t
2  x = (20)(cos 25 )(1.7232)
1
 y = − (9.81)(0.862)2 + (20)(sin 25 )(0.862)  x = 31.23m
2
 y = 3.641m  3.64m

vx = vo cos
 vx = (20)cos(25 )
 vx = 18.1261m / s
y
v y = − gt + v o sin 
 v y = −(9.81)(1.7232) + (20)sin(25 )
 v y = −8.4522m / s
1
y = − gt 2 + vo (sin  )t
2 v = (v x ) 2 + (v y ) 2
1
 0 = − (9.81)t 2 + (20)(sin 25 )t  v = (18.1261) 2 + (−8.4522) 2
2
 t = 1.72sec m
 v = 20
t = 0sec s

m = 7.5kg  = 19  = 0.25

y

F y =0
 N p − W sin  = 0
 N p = mg sin 
 N p = (7.5)(9.81)(cos19 )
 N p = 69.5665 N

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BASPHYS Quiz 1

T2
 Fx = ma Fx Fy
 W sin  − f = ma
−T1 cos60 T1 sin 60
 mg sin  −  N p = ma
T2 cos30 T2 sin 30
 (7.5)(9.81)(sin19 ) − (0.25)(69.5665) = (7.5)(a )
m
 a = 0.87 2 Fxnet = T2 cos30 − T1 cos60
s
 3 1
m = 0.6kg; = 60 ,30 0 = T2   − T1  
 2  2
 3
60 30
1
T1   = T2 
2
 T1 = T2 3 ( )
 2 
60 30 Fynet = T1 sin 60 + T2 sin 30 + Fweight
T1 T2  3 1
0 = T1   + T2   − 6.0 N
0.6kg  2  2
 3
Fweight = mg 6.0 N = T2 3  ( ) 1
 + T2  
2
 2 
6.0 N = 2T2 T2 = 3.0 N
T1 T2

T1
 m
Fweight = mg = (0.6kg )  −10 2  = −6.0 N
 s 

T1
T1 = T2 ( 3) T1 = 3.0 N ( 3)
T1 = 5.1962 N  5.20 N

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 Society of Young Engineers Towards Achieving Excellence
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BASPHYS Quiz 1

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