Question

A particle of mass 0.8 g is moving at a constant speed 3 x 10^2 ms Caleulate
the change in its momentum when a force of 5 N acts on it for 4 s.

Answer 1

GIVEN :-

• Mass of Particle = 0.8g

• Initial Velocity of the Particle (u) = 3 × 10²m/s = 300m/s

• Force Applied = 5N.

• Time Taken = 4s.

TO FIND :-

• Change in it's Momentum.

How To find

• As we know that Momentum is Product of Mass and Velocity So, In this question initial Velocity is given,so we have to find the Final Velocity to use the Below FORMULAE.

FORMULAE:-

• ${\boxed{\rm{Change\:in\: Momentum = mv - mu}}}$

• ${\boxed{\rm{ F = ma}}}$

• ${\boxed{\rm{ v = u+at}}}$

Now,

$\implies\rm{ F = ma}$

$\implies\rm{ F = 0.8\times{a}}$

$\implies\rm{ 5 = 0.0008\times{a}}$

$\implies\rm{ 50000= 8a}$

$\implies\rm{ a=\dffac{50000}{8}}$

$\implies\rm{a = 6,250m/s^-2}$

Now,

$\implies\rm{ v = u+at}$

$\implies\rm{ v = 3\times{10}^2 +6,250\times{4}}$

$\implies\rm{ v= 300 +250000}$

$\implies\rm{v = 250300}$

Now,

$\implies\rm{Change\:in\: momentum = mv-mu}$

$\implies\rm{Change\:in\: momentum = 0.0008\times{250300} - 0.0008\times{300}}$

$\implies\rm{Change\:in\: momentum = (200.24)-(0.24)}$

$\implies\rm{Change\:in\: momentum = 200m/s.}$

Hence, The change in momentum is 200m/s.