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

R=250 N

α = 38.86⁰

Step-by-step 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=√(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=(150)/(200)\\tan\alpha=0.75\\\alpha=38.86\ degrees`

R=250 N

α = 38.86⁰