Question

Which would require a greater force: accelerating a 2 kg mass at 5$m/{s^2}$ or a 4 kg mass at 2$m/{s^2}$?

Answer 1

Hint: Newton’s second law of motion gives the relation between the force applied on a body and the acceleration produced in that body. By finding out the amount of force in the two given cases, we can find out which force is greater.

Formula used:
Newton’s second law of motion is given as
\[F = ma\]

Complete step-by-step answer:
Let us consider the first case given to us. The mass of the object is given as
${m_1} = 2kg$
The amount of acceleration produced in this mass is given as
${a_1} = 5m/{s^2}$
The force which has produced this acceleration can be calculated by using Newton’s second law of motion which states that the magnitude of force applied on a body of certain mass is equal to product of the mass of the body and the amount of acceleration produced in that body. Therefore, for the first case, we can write that
${F_1} = {m_1}{a_1}$
Inserting the known values, we get
${F_1} = 2 \times 5 = 10N$
Similarly, in the second case, the mass of the object is given as
${m_2} = 4kg$
The amount of acceleration produced in this mass is given as
${a_2} = 2m/{s^2}$
Using Newton’s second law of motion, we can write that
${F_2} = {m_2}{a_2}$
Inserting the known values, we get
${F_2} = 4 \times 2 = 8N$
We can see that the force applied in the first case is greater than the force applied in the second case. Hence, accelerating a 2 kg mass at 5$m/{s^2}$ requires more force than accelerating a 4 kg mass at 2$m/{s^2}$.

Note: It should be noted that despite the mass being larger in the second case, the acceleration produced in it is smaller than the first case. Overall we can say that, the product of the mass and the acceleration produced in a mass decides the amount of force that is applied on the given mass.