Three men are trying to move a wardrobe. One pushes northward with a force of 100N; the second pushes eastward with a force of 173N; the third pushes in a direction 60 degrees west of south with a force of 200N. What is the resultant force on the wardrobe and it's direction?
To find the resultant force on the wardrobe, we need to calculate the sum of the forces acting in different directions.
First, let's break down the forces into their respective components. We can use the concept of vectors to do this.
1. The force pushing northward with 100N can be written as (0N, +100N) since it has no eastward component.
2. The force pushing eastward with 173N can be written as (+173N, 0N) since it has no northward component.
3. The force pushing in a direction 60 degrees west of south with a force of 200N can be resolved into its northward and eastward components. The northward component is given by 200N * sin(60°) = 200N * 0.866 = +173.2N, and the eastward component is given by 200N * cos(60°) = 200N * 0.5 = +100N. Thus, this force can be written as (+100N, -173.2N).
Now, we add the components of the forces together to find the resultant force:
Northward component: 0N + 173.2N + (-173.2N) = 0N
Eastward component: 173N + 100N - 100N = 173N
Thus, the resultant force on the wardrobe is (0N, 173N).
To find the overall magnitude of the resultant force, we can use the Pythagorean theorem:
Resultant force = sqrt((0N)^2 + (173N)^2) = sqrt(0N + 29929N^2) = sqrt(29929N^2) = 173N
Therefore, the magnitude of the resultant force is 173N.
To determine the direction of the resultant force, we can use trigonometry. The angle can be found using the inverse tangent (arctan) function:
Angle = arctan(173N/0N) = arctan(inf) = 90°
Since the northward component is zero, we can conclude that the resultant force is purely eastward, with a magnitude of 173N and a direction of 90 degrees east of north.
Therefore, the resultant force on the wardrobe is 173N in a direction 90 degrees east of north.
north at 100N = (0,100)
east at 173N = (173,0)
S60°W at 200N = (-173,-100)
add them up to get (0,0)
Extra credit --
Q: what are the names of the men?
A: Larry, Moe, Curly!