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)
___N
___°
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)
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°.