Question

The components of a force of 100 N acting at an angle of 30 degrees with the X -axis is

Answer 1

Magnitude of force, F = 100 N

angle with x axis, t = 30°

x component of force = F cos t = 100× cos(30) = 100 × √3/2 = 50√3 N

y component of force = F sin t = 100× sin(30) = 100 × 1/2 = 50 N

F = (50√3 i + 50 j) N

Answer 2

Given:

• Net force is 100 N
• Angle of force with X axis is 30°.

To find:

• The component of the net force along X and Y axis ?

Calculation:

The components of the force will be :

Along X axis :

$F_{x} = F_{net} \times \cos( \theta)$

$\implies F_{x} = 100 \times \cos( {30}^{ \circ} )$

$\implies F_{x} = 100 \times \dfrac{ \sqrt{3} }{2}$

$\implies F_{x} = 50 \sqrt{3} \: N$

Along Y axis :

$F_{y} = F_{net} \times \sin( \theta)$

$\implies F_{y} = 100\times \sin( {30}^{ \circ} )$

$\implies F_{y} = 100\times \dfrac{1}{2}$

$\implies F_{y} = 50 \: N$

So, the X axis component is 50√3 N and Y axis component is 50 N.