Question

which would require a greater force 2 kg mass at 5m/s2 or to 4 kg mass at 2 m/s2

Answer 1

First case:

Mass, m = 2 kg

Acceleration, $5 \ \mathrm{m} / \mathrm {s}^{2}$

Second case:

Mass, m = 4 kg

Acceleration, $2 \ \mathrm{m} / \mathrm {s}^{2}$

Solution:

The force is measured product of mass and acceleration so the force is directly dependent upon the mass of the body as well as the acceleration. So, the greater force required is compared by calculating force on each as follows,

$\text{Force} = \text{Mass} \times \text{Acceleration}$

$\text{Force} =\mathrm{m} \times \mathrm{a}$

For the first case,

$\mathrm{F}= 2 \times 5$

$F = 10N$

For the second case,

$\mathrm{F}= 4 \times 2$

$F = 8 N$

So, the first case has greater force required than the second case.

Answer 2

${ \huge{ \bold{\underline{ \underline{ \red{Solution:-}}}}}}$

$\large \star{\tt{\pink{Given:-}}}$

In 1st Case,

${\tt{Mass= 2kg}}$

${\tt{Acceleration = 5m/s^2}}$

In 2nd case,

${\tt{Mass = 4kg}}$

${\tt{Acceleration = 21m/s^2}}$

${ \large{ \bold{\underline{ \underline{ \orange{Concept:-}}}}}}$

The direction of the applied force is the direction of acceleration. As the force has both magnitude and direction,so it's a vector quantity.

${\tt{Force = Mass × Acceleration}}$${\tt{Force = ma}}$

For the first case,

${\tt{F = 2×5}}$

${\tt{F =10 N}}$

For the second case,

${\tt{F = 4×2}}$

${\tt{F = 8 N}}$

Hence,the first force is greater than the second required force.