Question

16. An object of mass 100 kg is accelerated uniformly from a velocity<br />of 5 ms-1 to 8 ms- in 6 s. Calculate the initial and final<br />momentum of the object. Also, find the magnitude of the force<br />exerted on the object.​

Answer 1

Explanation:

Given:

• Mass (m) = 100 kg
• Initial velocity (u) = 5 m/s
• Final velocity (v) = 8 m/s
• Time (t) = 6 seconds

To find:

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

Solution:

We know, $\blue{\tt{momentum(P)\:=\:mass(m)\:\times \:velocity(v)}}$.

So, the initial momentum = mu.

Where, m = mass

$\:\:\:\:\:\:\:\:\:\:$ u = initial velocity.

$\:$

$\Longrightarrow$ Initial momentum = 100 × 5

$\:$

$\Longrightarrow\:\sf{\underline{\underline{\therefore\:Initial\:momentum\:=\:500\:kg\:m/s.}}}$

$\:$

Now, final momentum = mass × final velocity.

$\:$

$\Longrightarrow$ Final momentum = 100 × 8

$\:$

$\Longrightarrow\:\sf{\underline{\underline{\therefore\:Final\:momentum\:=\:800\:kg\:m/s.}}}$

$\:$

We know that $\pink{\sf{Force(F)\:=\:mass(m)\:\times\:acceleration(a).}}$ We need to find acceleration for this.

We remember that $\sf{\underline{acceleration\:=\:\left(\dfrac{v\:-\:u}{t}\right)}}$

$\longrightarrow\:\sf{a\:=\:\left(\dfrac{8\:-\:5}{6}\right)}$

$\:$

$\longrightarrow\:\sf{a\:=\:\cancel{\dfrac{3}{6}}}$

$\:$

Hence, acceleration = 0.5 m/s².

Now, put the values in the formula for force.

$\:$

$\Longrightarrow$ F = 100 × 0.5

$\:$

$\Longrightarrow\:\sf{\underline{\underline{\therefore\:Force\:=\:50\:Newton.}}}$

Answer 2

$\Huge\mid{\overline { \underline{\sf{Answer}}}} \mid$

_____________________________________________________________________________________________

$\large \underline{\underline{\red{\frak{Given::}}}}$

$\mapsto \sf{Mass(m) \: of \: object=100kg}$

$\sf{ \mapsto{Initial \: velocity (u) \: of \: object=5m {s}^{ - 1} }}$

$\sf{ \mapsto{Final \: velocity (v) \: of \: object=8m {s}^{ - 1} }}$

$\sf{\mapsto{Time(t) \: taken \: to \: change \: in \: velocity=6 \: second}}$

${ \large {\underline{\underline{\pink{\frak{To \: find::}}}}}}$

$\sf{ \leadsto{Initial \: momentum(P{_1}) \: of \: object. }}$

$\sf{ \leadsto{Final \: momentum(P{_2}) \: of \: object. }}$

$\sf{ \leadsto{Force \: required \: to \: change \: in \: velocity \: of \: object. }}$

${ \large {\underline{\underline{\blue{\frak{Formula \: required::}}}}}}$

$\bullet{\fbox{ \bf{Momentum(P) \: of \: object =mass(m)\:of\:object×velocity(v)\:of\:object}}} \bullet$

$\bullet{ \boxed{ \bf{Acceleration(a)= \frac{Final \: velocity (v)-Initial \: velocity(u)}{Time (t) \: taken \: to \: change \: in \: velocity} }}} \bullet$

${ \large {\underline{\underline{\green{\frak{According \: to \: Question::}}}}}}$

$\sf{ \rightarrow{Initial \: momentum(P{_1}) \: of \: object = mass(m) \: of \: object× initial \: velocity(u) \: of \: object}}$

$\sf{ \implies{Initial \: momentum(P{_1}) \: of \: object = 100kg \times 5m {s}^{ - 1} }}$

$\sf{ \implies{Initial \: momentum(P{_1}) \: of \: object = 500kg•m {s}^{ - 1} }}$

_____________________________________________________________________________

$\sf{ \rightarrow{Final \: momentum(P{_2}) \: of \: object = mass(m) \: of \: object× final \: velocity(v) \: of \: object}}$

$\sf{ \implies{Final \: momentum(P{_2}) \: of \: object = 100kg \times 8m {s}^{ - 1} }}$

$\sf{ \implies{Final \: momentum(P{_2}) \: of \: object = 800kg•m {s}^{ - 1} }}$

______________________________________________________________________________

$\sf{ \rightarrow{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = mass(m) \: of \: object \times acceleration(a) \: of \: object}}$

$\sf{ \implies{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = mass(m) \: of \: object \times \frac{final \: velocity(v) \: of \: object - initial \: velocity(u) \: of \: object}{time(t)} }}$

$\sf{ \implies{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = 100kg \times \frac{8m {s}^{ - 1} - 5m {s}^{ - 1} }{6sec} }}$

$\sf{ \implies{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = 100kg \times \frac{ 3m{s}^{ - 1} }{6sec} }}$

$\sf{ \implies{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = 100kg \times 0.5m {s}^{ - 2} }}$

$\sf{ \implies{Force(F) \: required \: to \: change \: in \: velocity \: of \: object = 50N }}$

_____________________________________________________________________________

___________________________________________________________________________________________