Two movers are pushing a large crate with a force of 50.0 N each. One pushes north, the other east. What is the equilibrant force?
a. 71 N Southwest
b. 50 N Northeast
c. 100 N Southeast
d. 71 N Northeast
The resultant force is 71 NE
So, the equilibrant force is 71 SW
To find the equilibrant force, we need to find the vector sum of the two forces being applied by the movers.
First, let's represent the force applied by the mover pushing north as F₁, and the force applied by the mover pushing east as F₂.
The magnitude of each force is 50.0 N.
To find the equilibrant force, we can use the Pythagorean theorem to calculate the magnitude of the resultant force:
Magnitude of resultant force = √(F₁² + F₂²)
Magnitude of resultant force = √((50.0 N)² + (50.0 N)²)
Magnitude of resultant force = √(2500 N² + 2500 N²)
Magnitude of resultant force = √(5000 N²)
Magnitude of resultant force = 71 N (approximately)
Therefore, the correct answer is option d. 71 N Northeast.
To find the equilibrant force, we need to determine the net force acting on the crate. The net force is the vector sum of all the individual forces acting on the object.
In this case, one mover is pushing with a force of 50.0 N north, and the other mover is pushing with a force of 50.0 N east. Since these forces act in different directions, we need to add them as vectors to find the net force.
To add vectors, we can use the Pythagorean theorem and trigonometry. Let's break down the forces into their respective components:
The force pushing north has a vertical component of 50.0 N (since it is purely north) and a horizontal component of 0 N (since it is not in the east direction).
The force pushing east has a vertical component of 0 N (since it is not in the north direction) and a horizontal component of 50.0 N (since it is purely east).
Now, we can find the net force by adding the horizontal and vertical components separately.
The vertical component is (50.0 N) - (0 N) = 50.0 N.
The horizontal component is (50.0 N) - (0 N) = 50.0 N.
Using the Pythagorean theorem, we can find the magnitude of the net force:
Magnitude of the net force = sqrt(vertical component^2 + horizontal component^2)
= sqrt(50.0^2 + 50.0^2)
= sqrt(2500 + 2500)
= sqrt(5000)
≈ 70.71 N
Lastly, we need to determine the direction of the equilibrant force. Since the northward force and eastward force cancel each other out, the equilibrant force will be in the southeast direction (opposite to the resultant of the two forces).
Therefore, the correct answer is c. 100 N southeast.