Question

forces of 3, 4, 5, 6 and 25 act respective along the sides AB, BC, CD and DA along the diagonal AC of the square ABCD find their resultant.​

Answer 1

Answer:

Explanation:

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

​

 

4

155

​

=5P+50−  

4

125

​

 

⇒5P=  

4

155

​

+  

4

125

​

−50

⇒5P=  

4

280

​

−50=70−50=20

⇒P=4.