Question

How much momentum will an object of mass 10kg transfer to the floor it if falls from a height of 5m? ( g=10m/s) use v2=u2+2as

Answer 1

Answer:

Given:

Mass = 10 kg

Height = 5 m

To find:

Momentum transferred to floor after falling

Concept:

Whenever the ball is falling from that height and reaches the floor , it strikes the floor surface, changes it's direction of velocity and bounces back.

So the momentum change of ball is actually transferred to the floor.

Calculation:

Velocity just before hitting the floor :

$\bigstar \: \: {v}^{2} = {u}^{2} + 2gh$

$= > {v}^{2} = {0}^{2} + 2 \times (10) \times (5)$

$= > {v}^{2} = 100$

$= > v = 10 \: m {s}^{ - 1}$

Now considering completely in-elastic Collision between ball and floor :

Momentum before hitting ground :

$p1 = m(v1)$

$= > p1 = 10 \times (10) = 100 \: kgm {s}^{ - 1}$

Momentum after hitting ground:

$p2 = m(v2)$

$= > p2 = 10 \times ( 0)$

$= > p2 = 0 \: kgm {s}^{ - 1}$

So change in Momentum of ball:

$\Delta \: p = p2 - p1$

$= > \Delta \: p = - 0 - 100$

$= > \Delta \: p = - 100 \: kgm {s}^{ - 1}$

So momentum transferred to the ground will be equal and opposite to momentum change of ball :

So final answer is :

$\boxed{p_{(transferred)} = + 100 \: kgm {s}^{ - 1} }$

Answer 2

AnsweR :

• Momentum is 100 kgm/s

ExplanatioN :

• Mass (m) = 10 kg
• Height (h) = 5 m
• Initial velocity (u) = 0 m/s
• Acceleration (a) = 10 m/s²

Use 3rd ex of motion :

$\boxed{\sf{v^2 \: - \: u^2 \: = \: 2gh}} \\ \\ \longrightarrow \sf{v^2 \: - \: 0^2 \: = \: 2 \: \times \: 10 \: \times \: 5} \\ \\ \longrightarrow \sf{v^2 \: = \: 20 \: \times \: 5} \\ \\ \longrightarrow \sf{v^2 \: = \: 100} \\ \\ \longrightarrow \sf{v \: = \: \sqrt{100}} \\ \\ \longrightarrow \sf{v \: = \: 10} \\ \\ \underline{\underline{\sf{Velocity \: is \: 10 \: ms^{-1}}}}$

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Now, use formula for momentum

$\boxed{\sf{p \: = \: mv}} \\ \\ \longrightarrow \sf{p \: = \: 10 \: \times \: 10} \\ \\ \longrightarrow \sf{p \: = \: 100} \\ \\ \underline{\underline{\sf{Momentum \: is \: 100 \: kg ms^{-1}}}}$