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?

Answer 1

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