The diagram shows a metre stick suspended from its centre of gravity. A force of 4N acts on the stick at the 20cm mark. A force of FN acts on the stick at the 70 cm mark. The stick is balanced horizontally. Calculate force F.
Question
The diagram shows a metre stick suspended from its centre of gravity. A force of 4N acts on the stick at the 20cm mark. A force of FN acts on the stick at the 70 cm mark. The stick is balanced horizontally. Calculate force F.
Solution
To solve this problem, we need to understand that for the stick to be balanced, the sum of the moments on either side of the center of gravity must be equal. The moment is calculated as the force multiplied by the distance from the pivot (center of gravity).
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Identify the distances from the center of gravity: The force of 4N is 30cm (or 0.3m) from the center of gravity (50cm mark), and the force F is 20cm (or 0.2m) from the center of gravity.
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Set up the equation: The sum of the moments on either side of the center of gravity must be equal. So, we have 4N * 0.3m = F * 0.2m.
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Solve for F: Divide both sides of the equation by 0.2m to solve for F. F = (4N * 0.3m) / 0.2m = 6N.
So, the force F that acts on the stick at the 70 cm mark is 6N.
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