Question

Two movers push horizontally on a refrigerator. One pushes due north with a force of 150 N and the other pushes due east with a force of 200 N. Find the direction and magnitude of the resultant force on the refrigerator.

Answer 1

Answer:

R=250 N

α = 38.86⁰

Explanation:

Given that

Force ,F₁ = 150 N (Towards north  )

Force ,F₂ = 200 N ( Towards east )

We know that the angle between north and east direction is 90⁰ .

The resultant force R is given as

$R=\sqrt{F_1^2+F_2^2+2F_1F_2cos\theta$

We know that

cos 90⁰ =  0

That is why

$R=\sqrt{150^2+200^2}\\R=250\ N$

Therefore the magnitude of the forces will be 250  N.

The angle  from the horizontal of the resultant force = α

$tan\alpha=\dfrac{150}{200}\\tan\alpha=0.75\\\alpha=38.86\ degrees$

R=250 N

α = 38.86⁰