A 4 m uniform seesaw supports two children weighing 500 N and 350 N, respectively. The 500 N child is located 1.5 m from the center. What is the position of the 350 N child?
Question
A 4 m uniform seesaw supports two children weighing 500 N and 350 N, respectively. The 500 N child is located 1.5 m from the center. What is the position of the 350 N child?
Solution
To solve this problem, we need to use the principle of moments (or torques) which states that for an object to be in equilibrium (like the seesaw), the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
Step 1: Identify the forces and their distances from the pivot (center of the seesaw).
- The weight of the 500 N child acts 1.5 m from the pivot.
- The weight of the 350 N child acts at an unknown distance (x) from the pivot.
Step 2: Set up the equation for the moments about the pivot.
- The moment of the 500 N child is 500 N * 1.5 m = 750 Nm (acting clockwise).
- The moment of the 350 N child is 350 N * x m (acting anticlockwise).
Step 3: According to the principle of moments, these two moments must be equal for the seesaw to be balanced. So, we set up the equation 750 Nm = 350 N * x m.
Step 4: Solve the equation for x.
- x = 750 Nm / 350 N = 2.14 m.
So, the 350 N child should be located 2.14 m from the center of the seesaw to balance it.
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