In a rugby match 3 players huddle around a fourth player and push him. If they push with the following forces, what is the resultant force on him? 160 N 125, 140 N 35, and 220 N 200
To calculate the resultant force on the fourth player, we need to use vector addition. In vector addition, we add the forces together taking into account their magnitudes and directions.
Let's represent the forces as vectors:
Force 1 (160 N) in the direction of its push.
Force 2 (125 N) in the direction of its push.
Force 3 (140 N) in the direction of its push.
Force 4 (35 N) in the direction of its push.
Force 5 (220 N) in the direction of its push.
Now, we can add these forces together.
Step 1: Convert the forces into their respective x and y components.
The forces given do not have specific directions, so we assume they act along the x-axis or y-axis.
Force 1 (160 N) has an x-component of 160 N and a y-component of 0 N.
Force 2 (125 N) has an x-component of 125 N and a y-component of 0 N.
Force 3 (140 N) has an x-component of 140 N and a y-component of 0 N.
Force 4 (35 N) has an x-component of 0 N and a y-component of 35 N.
Force 5 (220 N) has an x-component of 0 N and a y-component of 220 N.
Step 2: Add the x and y components of the forces separately.
Sum of x-components = 160 N + 125 N + 140 N + 0 N + 0 N = 425 N
Sum of y-components = 0 N + 0 N + 0 N + 35 N + 220 N = 255 N
Step 3: Calculate the resultant force using the Pythagorean theorem.
The resultant force (R) can be calculated as follows:
R = √(Sum of x-components)^2 + (Sum of y-components)^2
R = √(425 N)^2 + (255 N)^2
R ≈ √(180,625 N^2 + 65,025 N^2)
R ≈ √245,650 N^2
R ≈ 495.63 N (rounded to two decimal places)
Therefore, the resultant force on the fourth player is approximately 495.63 N.