Question

The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when al
on it for 2
(a) What is the momentum before the force acts ?
(b) What is the momentum after the force acts 7
(c) What is the gain in momentum per second ?
(d) What is the value of the force ​

Answer 1

${\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}}$

( a ) Momentum before the force acts :

${\large{\underline{\purple{\rm{ 40 \ kg.\dfrac{m}{s}}}}}}$

( b ) Momentum after the force acts :

${\large{\underline{\purple{\rm{ 80 \ kg.\dfrac{m}{s}}}}}}$

( c ) Gain in momentum per second :

${\large{\underline{\purple{\rm{ 20 \ kg.\dfrac{m}{s}}}}}}$

( d ) The value of the force :

${\large{\underline{\purple{\rm{ 20 N.}}}}}$

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${\large{\underline{\pink{\sf{Given:}}}}}$

➛Mass of the body = 10 kg.

➛Initial velocity u = 4 m/s.

➛Final velocity v = 8 m/s.

➛Time t = 2s.

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${\large{\underline{\blue{\sf{To \ Find}}}}}$

( a ) Momentum before the force acts :

( b ) Momentum after the force acts :

( c ) Gain in momentum per second :

( d ) The value of the force :

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${\purple{\underline{\underline{\pink{\boxed{\boxed{\blue{\star{\sf Solution:}}}}}}}}}$

We are given,

➛Mass of the body ( m ) = 10 kg.

➛Initial velocity ( u ) = 4 m/s.

➛Final velocity ( v ) = 8 m/s.

➛Time t = 2s.

Now, Let's solve each Question one by one.

( a ) Momentum before the force acts :

We know ,

${\large{\orange{\boxed{\green{\star{ p_1 = m \times u }}}}}}$

= 10 x 4 = 40 kg.m/s

Momentum before the force acts : 40 kg.m/s

( b ) Momentum after the force acts :

${\large{\orange{\boxed{\green{\star{ p_2 = m \times v }}}}}}$

= 10 × 8 = 80 kg.m/s

Momentum after the force acts : 80 kg.m/s.

( c ) Gain in momentum per second :

${\large{\orange{\boxed{\green{\star{ Gain\:in\: momentum\:for\:2 \:sec = p_2 - p_1 }}}}}}$

= 80 - 40 = 40 kg.m/s

Gain in momentum per second : 40 / 2

Gain in momentum per second : 20 kg.m/s.

( d ) The value of the force :

$acceleration(a) = \frac{v - u}{t}$

$acceleration(a) = \frac{8 - 4}{2}$

acceleration : 2 m/s²

${\large{\orange{\boxed{\green{\star{Force = m \times a}}}}}}$

Force = 10 × 2

Force = 20 N.

The value of the force : 20 N.