Question

ABCDEF is a rectangular hexagon, forces of 3, P, Q, 5 and 4N are acting along AB, CA, AD, AE and FA respectively and are in equilibrium. Determine the value of P & Q.​

Answer 1

Answer:

Correct option is A)

ABCD is a rectangle in which AB=4 m and BC=3 m

Then, tanθ=

AB

BC

=

4

3

The forces 3,P,5,10 and Q newtons have the resultant R Newton as shown in the figure.

Rcosθ+5−3

=Qcosθ+2....(i)

and Rsinθ=P+10−Qsinθ....(ii)

and Q ABsinθ+5.BC=10.AB

or Q 4.(3/5)+5×3=10×4(∵sinθ=

5

3

and cosθ=

5

4

)

⇒

5

12

Q=40−15=25

⇒Q=

12

125

newton

Then, find R from Eq. (i) and P from Eq. (ii).

5

4R

=

12

125

×

5

4

+2

⇒4R=

3

125

+10=

3

155

⇒R=

12

155

and

12

155

×

5

3

=P+10−

12

125

×

5

3

and

12

155

×

5

3

=P+10−

12

125

×

5

3

4

155

=5P+50−

4

125

⇒5P=

4

155

+

4

125

−50

⇒5P=

4

280

−50=70−50=20

⇒P=4.

Explanation:

I think this the correct qst