Question

A 2 kg plate is kept suspended in air by allowing 10 marbles hitting per second with a speed v from the downward direction. If the mass of each marble is 20 g then determine v
no fools behavior only answer

Answer 1

Answer:

0.98m/s

Explanation:

Given that:

Mass of disc,M=10g=0.010kg

Mass of each marble,m=5g=0.005kg

Suppose the number of marbles striking the disc per second=n and velocity with which marbles strike disc is v.

Then Weight of disc acting downward=Mg

Change in velocity of marbles when they rebound =v−(−v)=2v

Therefore the change in momentum of each marble when it strikes the disc=m∗2v=2mv

and total momentum imparted per second to the disc=2mnv= The force exerted by the marbles in the upward direction

The disc will remain at rest if the net force acting on it is zero provided it is initially at rest.

Therefore for the disc to remain at rest,

Weight of disc=Upward force on it

=Mg=2mnv

v=

2mn

Mg

=

(2∗0.005∗10)

(0.010∗9.8)

=0.98m/s

Answer 2

Given:

A 2 kg plate is kept suspended in air by allowing 10 marbles hitting per second with a speed v from the downward direction. The mass of each marble is 20 g.

To find:

Value of "v" ?

Calculation:

The rate change of momentum of the marbles upon heating the plate will provide an upward force which should be equal and opposite to the weight of the plate.

• Let mass of marble be M , n represents total number of marbles hitting the plate, m is the mass of the plate.

• I am considering the fact that after hitting the plate the marble comes to rest.

$\rm \therefore \: F = mg$

$\rm \implies \: \dfrac{\Delta P}{\Delta t} = mg$

$\rm \implies \: \dfrac{n \bigg \{M(\Delta v) \bigg \}}{\Delta t} = mg$

$\rm \implies \: 10 \bigg \{ \dfrac{20}{1000} (v - 0) \bigg \} = 2 \times 10$

$\rm \implies \: 10 \bigg \{ \dfrac{20v}{1000}\bigg \} = 2 \times 10$

$\rm \implies \: 10 \bigg \{ \dfrac{v}{1000}\bigg \} =1$

$\rm \implies \: \bigg \{ \dfrac{v}{100}\bigg \} =1$

$\rm \implies \: v = 100 \: m {s}^{ - 1}$

So, Velocity of each marble is 100 m/s.