Question

An object of mass 100kg is accelerated uniformly from a velocity of 5m/s to 8m/s in 6 s.Calculate the i initial and final momentum and also calculate the force exerted on the objec t,

Answer 1

Answer :-

• Initial momentum = 500kg m/s

• Final momentum = 800kg m/s

• Force = 50N

Explanation :-

Given :

• Initial velocity,u = 5m/s

• Final velocity,v = 8m/s

• Mass of the object,m = 100kg

• Time taken,t = 6s

To Find :

• Initial momentum = ?

• Final momentum = ?

• Force = ?

Solution :

We know that,

$\sf{}Momentum=mass\times velocity$

Therefore,initial momentum = mass × velocity

$\sf{}\implies 100kg\times 5m/s$

$\sf{}\therefore 500kg\ m/s$

Final momentum = mass × velocity

$\sf{}\implies 100kg\times 8m/s$

$\sf{}\therefore 800kg\ m/s$

We know Force = Mass × Acceleration

But we don’t have the value of acceleration,so let’s find out acceleration first

According to the first equation of motion,

$\sf{}v=u+at$

$\sf{}\implies 8m/s = 5m/s + a \times 6s$

$\sf{}\implies 8m/s - 5m/s = a \times 6s$

$\sf{}\implies 3m/s = a \times 6s$

$\sf{}\implies \dfrac{3m/s}{6s} = a$

$\sf{}\therefore a=0.5m/s^2$

Now we know acceleration,so force exerted on the object:

$\sf{}\implies Force= 100kg\times 0.5m/s^2$

$\sf{}\implies Force= 50N$

Answer 2

Given:

• mass= 100kg
• u= 5m/s
• v= 8m/s
• t= 6s

━━━━━━━━━━━━━━━━━━

Need to find:

• Initial momentum=?
• Final momentum =?
• Force= ?

━━━━━━━━━━━━━━━━━━━

Solution:

We know,

P= m× v

$P_initial$= mass× initial velocity

$\implies\:P_initial$= 100× 5 kgm/s

$\red{\implies\:P_{initial}=500kgm/s}$

also

P= m× v

$P_finall$= mass× final velocity

$\implies\:P_final$= 100× 8 kgm/s

$\red{\implies\:P_{final}=800kgm/s}$

━━━━━━━━━━━━━━━━━━

From 1st equation of motion,

we know:

$v = u + at$

$\implies \: 8 = 5 + a \times 6$

$\implies \: 3 = 6a$

$\implies \: a = \dfrac{3}{6} \dfrac{m}{ {s}^{2} }$

$\implies \: a = 0.5 \dfrac{m}{{s}^{2} }$

Force= mass× Acceleration.

==> Forcs= 100kg× 0.5m/s^2

==>$\red{Force=50N}$