. A force of 5 N produces an acceleration of 8 m/s² on a mass m1 and an acceleration of 24 m/s on a mass m2. What acceleration would the same force provide if both the masses are tied together?
Question
. A force of 5 N produces an acceleration of 8 m/s² on a mass m1 and an acceleration of 24 m/s on a mass m2. What acceleration would the same force provide if both the masses are tied together?
Solution
To solve this problem, we first need to find the masses m1 and m2 using the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
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For mass m1: The force (F) is 5N and the acceleration (a) is 8 m/s². We rearrange the formula to solve for m (mass): m = F/a. So, m1 = 5N / 8 m/s² = 0.625 kg.
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For mass m2: The force (F) is 5N and the acceleration (a) is 24 m/s². Again, we rearrange the formula to solve for m (mass): m = F/a. So, m2 = 5N / 24 m/s² = 0.208 kg.
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Now, if both masses are tied together, their total mass (M) would be m1 + m2 = 0.625 kg + 0.208 kg = 0.833 kg.
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To find the acceleration (A) of this combined mass under the same force, we use the formula A = F/M. So, A = 5N / 0.833 kg = 6 m/s².
Therefore, the same force would provide an acceleration of 6 m/s² if both the masses are tied together.
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