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Question
Derive the unit of force using the second law of motion. A force of 5 N produces an acceleration of 8 m s–2 on a mass m1 and an acceleration of 24 m s–2 on a mass m2. What acceleration would the same force provide if both the masses are tied together?
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Solution
Using the relationship F = ma
If m is measured in kg and a is measured in ms−1
Then the unit of force is kg ms−2
1 kg ms−2 = 1 N
F = 5N, a1 = 8 ms−2 , a2 = 24 ms−2
∴ `m_1 = F/a_1 = 5/8` kg and `"m"_2 = F/a_2 = 5/24` kg
Now, total mass when both the masses are tied together,
m = m1 + m2 = `(5/8 + 5/24)` kg
= `((15 + 5)/24) "kg" = 20/24 "kg" = 5/6 "kg"`
∴ Acceleration, a = `F/m`
= `5/(5//6)`
= 6 m/s2
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