Question

i) Newton's first law of motion gives a qualitative definition of force. Justify.
ii) The figure represents two bodies of masses $10kg$ and $15kg$, moving with an initial velocity of $10m{s}^{-1}$ and $5m{s}^{-1}$ respectively. They collide with each other. After collision, they move with velocities $4m{s}^{-1}$ and $9m{s}^{-1}$ respectively. The time of collision is $2s$.
Now calculate $F_1$ and $F_2$

Answer 1

(i) Newton's first law states that an object will remains at rest or in uniform motion in a straight line unless acted upon external force.

Hence motion of 10kg and 15kg object is changes from 10m/s to 4m/s and 5m/s to 9m/s therefore some external force act on each other that is $F_1$ and $F_2$ or $F_1=+F_2$

(ii) change in momentum = impulse = Fdt

For 10kg mass

$10\times 10-4\times 10=F_2\times 2$

$F_2=30N$

for 15kg mass

$15\times 5-15\times 9=F_{1}t$

$75-135=F_1\times 2\Rightarrow F_1=+30N$