four forces act an object: 1000n at 0°, 80n at 90°, 50n at 180° and 20n at 270°. determine the net force
the forces are
<1000,0>, <0,80>, <-50,0>, <0,-20>
So, just add them up to get <950,60>
Why do I think 1000 is a typo?
Fn = 1000N[0o] + 80N[90o] + 50N[180o] + 20N[270o],
Fn = 1000 + 80i - 50 - 20i = 950 + 60i = 952N[3.60] = net force.
To determine the net force acting on an object, we need to calculate the vector sum of all the given forces. Each force is made up of both magnitude and direction.
Given forces:
1) 1000N at 0°
2) 80N at 90°
3) 50N at 180°
4) 20N at 270°
Step 1: Convert the forces into vector components.
To add the forces together, we need to break them down into their horizontal (x-axis) and vertical (y-axis) components.
Force 1: 1000N at 0°
- The horizontal component is 1000N * cos(0°) = 1000N * 1 = 1000N
- The vertical component is 1000N * sin(0°) = 1000N * 0 = 0N
Force 2: 80N at 90°
- The horizontal component is 80N * cos(90°) = 80N * 0 = 0N
- The vertical component is 80N * sin(90°) = 80N * 1 = 80N
Force 3: 50N at 180°
- The horizontal component is 50N * cos(180°) = 50N * -1 = -50N
- The vertical component is 50N * sin(180°) = 50N * 0 = 0N
Force 4: 20N at 270°
- The horizontal component is 20N * cos(270°) = 20N * 0 = 0N
- The vertical component is 20N * sin(270°) = 20N * -1 = -20N
Step 2: Add up the vector components.
To get the net force, we add the horizontal components and the vertical components separately.
Horizontal component: 1000N + 0N - 50N + 0N = 950N
Vertical component: 0N + 80N + 0N - 20N = 60N
Step 3: Calculate the resultant force.
Using the Pythagorean theorem, we can find the magnitude of the net force by taking the square root of the sum of the squares of the horizontal and vertical components.
Magnitude of net force = √(Horizontal^2 + Vertical^2)
= √(950N^2 + 60N^2)
= √(902,500N^2 + 3,600N^2)
= √906,100N^2
≈ 952.2N
The net force acting on the object is approximately 952.2N.