A force of 5 N gives a mass m 1 . an acceleration of 10 m s −2 and a mass m 2 . an acceleration of 20 m s −2 . What acceleration would it give if both the masses were tied together?
Question
A force of 5 N gives a mass m 1 . an acceleration of 10 m s −2 and a mass m 2 . an acceleration of 20 m s −2 . What acceleration would it give if both the masses were tied together?
Solution
The problem can be solved using Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).
First, let's find the masses m1 and m2.
Given that F = 5N and a1 = 10 m/s^2 for mass m1, we can rearrange the formula to find m1 = F/a1 = 5N / 10 m/s^2 = 0.5 kg.
Similarly, given that F = 5N and a2 = 20 m/s^2 for mass m2, we can find m2 = F/a2 = 5N / 20 m/s^2 = 0.25 kg.
Now, if both masses m1 and m2 are tied together, their total mass M is m1 + m2 = 0.5 kg + 0.25 kg = 0.75 kg.
We can now find the acceleration A of the combined masses under the force F. Using the formula A = F/M, we get A = 5N / 0.75 kg = 6.67 m/s^2.
So, if both the masses were tied together, the force would give them an acceleration of 6.67 m/s^2.
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