Two forces are exerted on an object. A 32 N force acts at 220° and a 53 N force acts at 315°. What are the magnitude and direction of the equilibrant?

Find the resultant first:

R=32cos220N + 32sin220E + 53Cos315N+53Sin315E

combine the E, and N

Then resultant is at an angle arctanE/N, of magnitude sqrt( Ecomponent^2+Ncomponent^2)

for the equilibrant, add 180 degrees to the resultant

You did this question so wrong it’s insane

To find the magnitude and direction of the equilibrant, we first need to calculate the resultant force of the two given forces. The equilibrant is the force required to balance out the resultant force and bring the object into equilibrium.

To calculate the resultant force, we can break down each force into its x and y components using trigonometry.

For the 32 N force at 220°:
- The x-component = 32 N * cos(220°)
- The y-component = 32 N * sin(220°)

For the 53 N force at 315°:
- The x-component = 53 N * cos(315°)
- The y-component = 53 N * sin(315°)

Next, we add up the x-components and the y-components separately. This will give us the resultant force.

Resultant force in the x-direction = sum of x-components
Resultant force in the y-direction = sum of y-components

Once we have the resultant force, we can find the magnitude and direction of the equilibrant.

Magnitude of the equilibrant = magnitude of the resultant force

Direction of the equilibrant = direction of the resultant force + 180°

Now let's perform the calculations.

For the 32 N force at 220°:
- The x-component = 32 N * cos(220°) = -26.76 N (negative because it acts in the opposite direction of the positive x-axis)
- The y-component = 32 N * sin(220°) = -11.28 N (negative because it acts in the opposite direction of the positive y-axis)

For the 53 N force at 315°:
- The x-component = 53 N * cos(315°) = 37.59 N
- The y-component = 53 N * sin(315°) = -37.59 N (negative because it acts in the opposite direction of the positive y-axis)

Resultant force in the x-direction = sum of x-components = -26.76 N + 37.59 N = 10.83 N
Resultant force in the y-direction = sum of y-components = -11.28 N - 37.59 N = -48.87 N

Magnitude of the resultant force = sqrt((Resultant force in the x-direction)^2 + (Resultant force in the y-direction)^2)
= sqrt((10.83 N)^2 + (-48.87 N)^2) ≈ 50.03 N

Direction of the resultant force = arctan(Resultant force in the y-direction / Resultant force in the x-direction)
= arctan((-48.87 N) / (10.83 N)) ≈ -78.77°

Magnitude of the equilibrant = magnitude of the resultant force ≈ 50.03 N

Direction of the equilibrant = direction of the resultant force + 180°
= -78.77° + 180° ≈ 101.23°

Therefore, the magnitude of the equilibrant is approximately 50.03 N, and its direction is approximately 101.23°.