Question

A bullet fire of mass 0.012kg and horizantal speed 70m/s Twice a black of wood of mass 0.4kg and instant come to rest with respect to black The black is suspended from ceiling bymeans of thin wire calculate the height to which height rise also estimate the height

Answer 1

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Here's the answer:

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A bullet fire of mass 0.012kg and horizontally speed 70m/s strikes a block of wood of mass 0.4kg and instant come to rest with respect to block. The block is suspended from ceiling by means of thin wire. Calculate the height to which height rise

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The given system consists :

BULLET, WOODEN BLOCK

Given,

Mass of bullet m1 = 0.012 kg

Initial Speed of the bullet u1 = 70 m/s

Mass of wooden block m2 = 0.4 kg

Initial Speed of Wooden block u2 = 0
{°•° Wooden block is at Rest initially }

Let final velocity of the system of bullet and the bag be v

¶¶¶ According to Law of Conservation of Momentum,
The total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

i. e.,
$m_{1}u_{1} + m_{2}u_{2} = (m1 + m2)v$

Substitute values,

=> (0.012×70) + (0.4×0) = (0.012+0.4)v

=> 0.412v = 0.84

=> v = 0.84/0.412 = 2.04 m/s

For the system of bullet and wooden block,

Mass of the system m' = 0.4+0.012 = 0.412 kg
Velocity of system = v = 2.04 m/s

let h be the height Upton which the system rises

¶¶¶ According to Law of conservation of Energy,
Potential Energy at Highest point = Kinetic Energy at Lowest point.

i.e.,
$m'gh = \frac{1}{2}m'v^{2}$

=> $h = \frac{v^{2}}{2g}$

h = (2.04)²/(2×9.8)

{°•° g = 9.8 m/s}

=> h = 0.2123 m

•°• The wooden block will rise Upton 0.2123 m

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