Question

For two forces P and Q acting at a point, maximum resultant is 2000N and minimum magnitude of resultant is 800N. Find values of P and Q.​

Answer 1

GiveN :-

• For two forces P and Q acting at a point, maximum resultant is 2000N and minimum magnitude of resultant is 800N .

To FinD:-

• The values of P and Q.

SolutioN :-

According to the Question , Maximum Resultant is 2000N and minimum is 800N . We need to find the values of P and Q .

$\sf\to | \vec{P }+ \vec{Q }| = 2000N$

$\sf\to | \vec{P }- \vec{Q }| = 800N$

Here we are assuming that , $\sf\vec{P}> \vec{Q}$

On adding both the equations we get ,

$\sf:\implies | \vec{P }+ \vec{Q }| + | \vec{P }- \vec{Q }| =( 2000N+800)N \\\\\sf:\implies 2\vec{P}= 2800 N \\\\\sf:\implies \vec{P}=\dfrac{2800N}{2}\\\\\sf:\implies\boxed{\pink{\frak{\vec{P}= 1400 \ Newtons }}}$

On putting this value in equation (1) we have Q = (2000-1400) N = 600N . Hence the vector P is 1400N and vector Q is 600 N .

Answer 2

Concept:

The push or pull on a mass-containing object that alters its velocity is referred to as force.

Resultant force: A system of forces and torques acting on a rigid body can be combined by vector addition to produce a single force and related torque.

Given:

The two forces P and Q.

The maximum resultant is 2000N and the minimum resultant is 800 N.

Find:

The value of P and Q.

Solution:

The maximum resultant force will be:

$P+Q=2000N$

Therefore, $P=2000-Q$

The minimum resultant force will be:

$P-Q=800N$

Therefore, $P=800+Q$

Form both the equations:

$2000-Q=800+Q\\2Q=1200\\Q=600N$

Substituting the value in $P=800+Q$,

$P=800+600\\P=1400N$

Hence, the value of P is 1400, and the value of Q is 600.

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