Elective Physics 10 Vectors Worksheet : Vector Operations worksheet (new versio… · Elective...

Elective Physics 10 Vectors Worksheet : Vector Operations

1

2A

-B

1.

-A 2B

-B+2A

2B-A

-B

A

A-B

a) c)

b)

Elective Physics 10 Vectors Worksheet : Vector Operations

2

2.3A

B

-C 3A+B-C

-2A

BC

B+C-2A

a)

b)

Elective Physics 10 Vectors Worksheet : Vector Operations

3

3.

C-2B

-C

-2B B-B

-B

A+BA

a)2B -A

2B-A

b)

c)

BC

B+C

Elective Physics 10 Vectors Worksheet : Vector Operations

4

4.

A

B

C DE

R

R 2 = 22 +42 ⇒ R 2 = 4+ 16R 2 = 20⇒ R = 2 5 cm

4 cm

2 cm

R

Elective Physics 10 Vectors Worksheet : Vector Operations

5

5.

B

A

C

D

R

E

E

E2 = 22 +42 ⇒E2 = 4+ 16E2 = 20⇒E = 2 5 cm

4 cm

2 cm

Elective Physics 10 Vectors Worksheet : Vector Operations

6

6.

-CB+C

B

a) the magnitude of

vector B is 2 cm

b)B

A+B

Athe magnitude

of vector A is

4 cm

Elective Physics 10 Vectors Worksheet : Vector Operations

7

7.

A-BO

A+B 2A

2A A

The magnitude of

vector A is 2 cm

Elective Physics 10 Vectors Worksheet : Vector Operations

8

8.

A+B B+C

A+C

2A+2B+2C

A+B+C

R

Elective Physics 10 Vectors Worksheet : Vector Operations

9

9.

3 m1 m

2 m

2 m

2 m2 2 m

2 2 m

45o

45o

Step-1

Step-2

Step-3

45o

2 2 m

2 2 m

45o

4 m 4 m

4 m

Step-4

R=4 m

60o

60o60o

Elective Physics 10 Vectors Worksheet : Vector Operations

10

10.

A

6 N

3 N

3 N120o 120o

Step-1 : divide vector A into two equal vectors.

Step-2

3 N 120o

3 N

3 N

Step-3

60o

3 N

60o60o

3 N

60o60o

3 3 N

3 3 N

3 3 N

R=9 NStep-4

+x

+y

Elective Physics 10 Vectors Worksheet : Vector Operations

11

11.

8 N 8 N

8 N

+y

+x

Step-1

60o60o

120o

Step-2

12 N

+x60o

60o

+y

60o

4 3 N 4 3 N

Step-3

8 N

12 N

4 N

Step-4

4 N

3 N

R=5 m

Elective Physics 10 Vectors Worksheet : Vector Operations

12

12.

East

North

West

South

53o

A

B

20 m

4 m

-B

4 m Ax

Ay

Ax=A.cos53o=(20).(0,6)=12 m

Ay=A.sin53o=(20).(0,8)=16 m

x-component y-component

A

-B

R

+12 m +16 m

0 -4 m

+12 m +12 m

12 m

12 m

R

Rx

Ry

R = 12 2 m

Elective Physics 10 Vectors Worksheet : Vector Operations

13

13.

East

North

West

South

53o

BA

C20 paces

15 paces 25 paces

Bx=B.sin53o=(25).(0,8)=20 paces

By=B.cos53o=(20).(0,6)=15 paces

x-component y-component

C

A

B

0 +15 paces

+20 paces +15 paces

+20 paces 0

R +40 paces +30 paces

30 paces

40 paces

R

Rx

Ry

R=50 paces

Elective Physics 10 Vectors Worksheet : Vector Operations

14

14.

Bx=B.cos53o=(20).(0,6)=12 N

By=B.sin53o=(20).(0,8)=16 N

Ax=A.cos37o=(10).(0,8)=8 N

Ay=A.sin37o=(10).(0,6)=6 N

x-component y-component

A

B

R

-8 N -6 N

+12 N +16 m

+4 N +10 N

R 2 = 42 + 102

R 2 = 16+ 100R 2 = 116⇒

R = 2 29 N

Elective Physics 10 Vectors Worksheet : Vector Operations

15

15. 3 N + 4 N < 8 N

So these vectors cannot form a triangle. Then the magnitude of the resultant vector cannot be equal to

zero.

16.x-component y-component

a

b+2a

-1 -1

+2 +2

-2 0

-2a

b

(-2a)(b+2a)+ = b

0 +2

So, vector “b” is “2”.

Elective Physics 10 Vectors Worksheet : Vector Operations

16

17.x-component y-component

2a

2 0

-1 -2

+1 -2

c-2a

a-b

+ =

0 +2

So, vector “c” is “3”.

a+b

(a+b) (a-b) 2a

2a +(c-2a)= c

c +1 0

Elective Physics 10 Vectors Worksheet : Vector Operations

17

18.

=0(K+L+M)

=M -(K+L)

So “4” is the vector “M”.

Elective Physics 10 Vectors Worksheet : Vector Operations

18

19.Vectors N and L are in the same line of action. So,

their resultant vector has a magnitude of 4 m and it is in the same direction as vector N.

Vectors K and M are in the same line of action. So, their resultant vector has a magnitude of 15 m and it

is in the same direction as vector M.

We can use the law of cosines to add these two vectors by using tip-to-tail method. The angle between them

is 530.

R2=(4)2+(15)2-(2.4.15.cos 530)

R2=(16)+(225)-(120.(0,6))

R2=(241)-(72))

R2=169

R=13 m

Elective Physics 10 Vectors Worksheet : Vector Operations

19

20.

R=F1+F2+F3

F2+F3 =F1

R=F1+F1=2F1

R=2F1=2F

21.R=K-L+M-N+P

R=-N-N=-2N

K-L+M+P =-N

Elective Physics 10 Vectors Worksheet : Vector Operations

20

22.

4 N and 6 N are in the same line of action. So, their resultant vector has a magnitude of 2 N

and it is in the same direction as 6 N.

3 N and 5 N are in the same line of action. So, their resultant vector has a magnitude of 2 N

and it is in the same direction as 5 N.

45o 45o

2 N2 N

2 N

2 N

(2 2)2

R

R2=(2)2+

R2=4+8=12

R=2 3 N

2 2 N

Elective Physics 10 Vectors Worksheet : Vector Operations

21

23. F3

F2F1

F4a

F4.cosa+F1=F3

F4.sina

F4.sina=F2 then F4>F2

Only statement-II is absolutely correct.

For statements I & III, we cannot say anything about being absolutely correct.

If R=0 then

Elective Physics 10 Vectors Worksheet : Vector Operations

22

24.

-F2-F3

F3 +2F2

F2

F2+F3

-F2

F3

F3=2 2 units

Elective Physics 10 Vectors Worksheet : Vector Operations

23

25.

99 N

99 N

99 N

1200

1200

1200

R=0

1 N

2 N

12006001 N 2 N

R

R2=(1)2+(2)2-(2.1.2.cos600)

R2=(1)+(4)-(2.1.2.(1/2))

R2=(5)-(2)

R2=3

R= 3 N

by using the law of cosines;

Elective Physics 10 Vectors Worksheet : Vector Operations

24

26.

b + d = 0

a = c

R = 2a or R=2c

27.

3 N

4 N

8 N

6 N

3 N

4 N

R

R=5 N

Elective Physics 10 Vectors Worksheet : Vector Operations

25

28.

12 N

37o

53o

15 N

12 N

9 N

a

21 N

21 N

R

R=21 2 N

x

cos530=a/x

53o

12 N

a

x

53o

sin530=12/x

3/4=a/12

a=9 N

0,6

0,8

Elective Physics 10 Vectors Worksheet : Vector Operations

26

29.

a + b + c + d = e

R = 2e

R = a + b + c + d + e

30.

20 - 10 = 10 N

the angle between 10 N & 10 N is 1200.

their resultant is 10 N upward (to +y)

R=30-10=20 N (to -y)

Elective Physics 10 Vectors Worksheet : Vector Operations

27

31.x-component y-component

M

+2 0

0 +1K

-1 -1

-K+L

+1 +1

L +2 +1

K+L+M

So, the vector “5” is the resultant vector of K+L+M

Elective Physics 10 Vectors Worksheet : Vector Operations

28

32.

R1= 3 F1 R2= 2 F2 R3=F3

The magnitudes of the resultant forces of the given forces are

R1= R2= R3

3 F1 2 F2 F3= =

F3 F2 F1> >

Elective Physics 10 Vectors Worksheet : Vector Operations

29

33.

The magnitudes of the two vector that are added are equal to each other.

If the angle between them gets smaller, the magnitude of their resultant vector would be

greater.

R3 R2 R1> >

34.

Rmax = A+B=10 m

Rmin = A-B=2 m

A = 6 m

B = 4 m

Elective Physics 10 Vectors Worksheet : Vector Operations

30

35. K

L

-P

-M

N

I.

Correct

II.

-LWrong

N-L=-PCorrect formIII. -K

M

P

-N

Correct

N-L=P

-M

Statements I and III are correct

Elective Physics 10 Vectors Worksheet : Vector Operations

31

36.a

b

3c/2

d

The sum of vectors “a” and “b” is equal to “3c/2”. Statement I is wrong.

Vectors “b” and “d” are in different directions but their magnitudes are equal. Statement II is

correct.

b

c

The sum of vectors “b” and “d” is equal to vector “c”. Statement III is correct.

Statements II and III are correct.