Question

If 2N, 4N and 5N forces are to be applied on object so that the net force is minimum then apply the

forces and find the net force.​

Answer 1

Given:

There are three forces 2 N, 4 N and 5 N are to be applied on object so that the net force is minimum. Then apply the forces.

To Find:

What is the value of minimum force?

Solution:

​We know that for maximum value of resultant of group of a force. All force line of action should along a same line and same direction:

From given value of group of forces, maximum value of force is given below:

Maximum value of force$\mathbf{=F_{max}=2+4+5}$

Maximum value of force $\mathbf{=F_{max}=11\ N}$

In same way for minimum value of resultant of group of force. Some group of  force should be same direction along a line, while other group of force should be opposite direction along same line. Such that resultant in minimum:

From group of 2 N , 4 N and 5 N:

We take one group of 2 N and 4 N, then their resultant is:

$\mathbf{F_{R_{1}}=2+4=6\ N}$

Now remaining force will left as 5 N, now taking 5 N just opposite to $\mathbf{F_{R_{1}}}$:

Now resultant force of 5 N and  $\mathbf{F_{R_{1}}}$ will be minimum:

Minimum value of force $\mathbf{=F_{min}=F_{R_{1}}-5}$

Minimum value of force $\mathbf{=F_{min}=6-5}$

Minimum value of force $\mathbf{=F_{min}=1 \ N}$

Means minimum value of resultant of 2 N, 4 N and 5 N will 1 N.