Question

the speed of a car of mass 2000kg increases from 50m/s to 70m/s.caluculate the change in momentum.

Answer 1

✪ Firstly let us understand the concept!

✴️ We know that, momentum, p is the product of mass, m and velocity, v of a body. Momentum is a vector quantity. Momentum can be negative too. The SI unit of momentum is kg m/s.

✴ ️Change in momentum: To calculate the change in momentum we have to find initial and final momentum then we have to subtract final momentum and initial momentum.

Now let's begin!

Provided that:

• Mass of the car = 2000 kg.
• Initial velocity = 50 mps.
• Final velocity = 70 mps.

To calculate:

• The change in momentum

Solution: The change in momentum = 40,000 kg m/s

Using concepts:

• Initial momentum formula
• Final momentum formula
• Change in momentum formula

Using formulas:

† Initial momentum formula:

• ${\small{\underline{\boxed{\pmb{\sf{p \: = mu}}}}}}$

† Final momentum formula:

• ${\small{\underline{\boxed{\pmb{\sf{p' \: = mv}}}}}}$

† Change in momentum formula:

• ${\small{\underline{\boxed{\pmb{\sf{\Delta \: = p' - p}}}}}}$

Where, m denotes mass, u denotes initial velocity, v denotes final velocity, p denotes initial momentum, p' denotes final momentum and ∆p denotes change in momentum.

Required solution:

✡️ Firstly by using formula to calculate initial momentum let us find out the initial momentum.

${\sf{:\implies p \: = mu}}$

${\sf{:\implies p \: = 2000(50)}}$

${\sf{:\implies p \: = 1,00,000 \: kg \: ms^{-1}}}$

${\sf{:\implies Initial \: momentum \: = 1,00,000 \: kg \: ms^{-1}}}$

$\quad \quad{\pmb{\sf{\underline{Therefore, \: initial \: momentum \: = 1,00,000 \: kg \: ms^{-1}}}}}$

✡️ Now by using formula to calculate final momentum let us find out the final momentum.

${\sf{:\implies p' \: = mv}}$

${\sf{:\implies p' \: = 2000(70)}}$

${\sf{:\implies p' \: = 1,40,000 \: kg \: ms^{-1}}}$

$\quad \quad{\pmb{\sf{\underline{Therefore, \: final \: momentum \: = 1,40,000 \: kg \: ms^{-1}}}}}$

✡️ Now by using change in momentum formula let us solve this whole question!

${\sf{:\implies \Delta p \: = mv - mu}}$

${\sf{:\implies \Delta p \: = p' - p}}$

${\sf{:\implies \Delta p \: = 1,40,000 - 1,00,000}}$

${\sf{:\implies \Delta p \: = 40,000 \: kg \: ms^{-1}}}$

$\quad \quad{\pmb{\sf{\underline{Therefore, \: change \: in \: momentum \: = 40,000 \: kg \: ms^{-1}}}}}$

Answer 2

Question:

• the speed of a car of mass 2000kg increases from 50m/s to 70m/s.caluculate the change in momentum.

Answer:

• The change in momentum is 40,000 kgm /s

Explanation:

Given that:

• the speed of a car of mass 2000kg increases from 50m/s to 70m/s.

To calculate:

• The change in momentum

Formula used:

${\bigstar \; {\underline{\boxed{\bf{\triangle \vec{ P} = \vec{P_1} - \vec{P_2} }}}}}$

Required solution:

• Using formula to find momentum

${\leadsto\; {\pink{\boxed{\bf{\vec{ P} = {m} \vec{v} }}}}}$

★ Where,

• $\vec{\sf P }$ Stands for momentum
• M Stands for mass of the body
• $\vec{\sf v }$ Stands for velocity

★ Here,

• The change in momentum will be

${\leadsto\; {\pink{\boxed{\bf{\vec{ P} = {m} \vec{v_2} -{m} \vec{v_1} }}}}}$

★ we know that ,

• Mass of the truck is 2,000 kg
• Velocity ₁ of the truck is 50 m/s
• Velocity ₂ of the truck is 70 m/s

★ Plugging in the values,

• Let's firstly find out the initial momentum

${:\implies}\sf P_1 = mv_1$

${:\implies}\sf P_1 = 2,000 kg \times 50 m/s$

${:\implies}\sf P_1 = 1,00,000 kgm/s$

• Henceforth the initial momentum of the truck is 1,00,000 kgm/s

~ Now let's find the final momentum of the truck

${:\implies}\sf P_2 = mv_2$

${:\implies}\sf P_2 = 2,000kg\times 70 m/s$

${:\implies}\sf P_2 = 1,40,000 kgm/s$

$\;\; \;\; \;\; {\pmb{\sf{ Now ,\; Let's \: find\: the\; change \;in\; momentum}}}$

~ Subtract initial momentum from the final momentum

${:\implies}\sf \triangle P_{change}= mv_2 - mv_1$

${:\implies}\sf \triangle P_{change}= 1,40,000kgm/s- 1,00,000kgm/s$

${:\implies}\sf \triangle P_{change}= 40,000 kgm/s$

★Therefore,

• The change in momentum of the truck is 40,000 kgm/s

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