Question

Define momentum of a body.

How much momentum will a body of mass 200g transfer to the floor if it falls from a

height of 180 cm? Take its downward acceleration to be 10m/s2

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Answer 1

Given : a body of mass 200g falls from a height of 180 cm

g = 10 m/s²

To Find : How much momentum  will be transferred to floor

Solution:

momentum is the product of the mass and velocity of an object.

momentum = P

mass = m

velocity = v

P = mv

m = 200 g = 0.2  kg

h = 180 cm = 1.8 m

g = 10  m/s²

V² - U² = 2aS

U = 0  

a = g = 10

S = h = 1.8

V = ?

V² - 0 = 2(10)(1.8)

=> V² = 6

=> V = 6 m/s

Momentum = 0.2 * 6  = 1.2  kgm/s

Assuming body will be at rest after reaching floor

Then momentum transferred to floor will be 1.2 kgm/s

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Answer 2

• MOMENTUM is defined as a vector quantity characterised by the product of mass and velocity vector.

In order to solve these questions, first calculate final velocity of object :

${v}^{2} = {u}^{2} + 2gh$

$\implies {v}^{2} = {0}^{2} +( 2 \times 10 \times 1.8)$

$\implies {v}^{2} = 36$

$\implies v = 6 \: m {s}^{ - 1}$

• Now, just after touching the ground, velocity becomes zero. So, final momentum also becomes zero.

Momentum Change of object:

$\Delta P = 0.2 \times (0 - 6)$

$\implies \Delta P = 0.2 \times ( - 6)$

$\implies \Delta P = - 1.2 \: kgm {s}^{ - 1}$

• Now, momentum transferred to ground will be negative of the momentum change of object.

$\implies P_{ground} = - \Delta P$

$\implies P_{ground} = - ( - 1.2)$

$\implies P_{ground} = 1.2 \: kgm {s}^{ - 1}$

So, momentum transferred to ground is 1.2 kgm/s.