Aball of mass 2 kg moving at 6 m/s collides directly with another ball of mass 3 kg travelling in the same direction at 4 m/s. find the speed of each ball after impact and the loss in kinetic energy if the coefficient of restitution is equal to 3/4.

v₁ = 3.9 m/s

v₂ = 5.4 m/s

The loss in the kinetic energy = 1.05 J

Explanation:

Given:

mass, m₁ = 2 kg

m₂ = 3 kg

initial speed of mass m₁, u₁ = 6 m/s

Initial speed of the mass m₂, u₂ = 4 m/s

coefficient of restitution, e = (3/4)

let, the final speed of mass m₁ and m₂ be v₁ and v₂ respectively

Now,

on substituting the values, we get

or

1.5 = v₂ - v₁  

or

v₂ = 1.5 + v₁

also,

from the conservation of momentum, we have

( 2 × 6 ) + ( 3 × 4 ) = ( 2 × v₁ ) + ( 3 × v₂ )

or

24 = 2 × v₁ + ( 3 × ( 1.5 + v₁ ) )

or

24 = 2 × v₁ + 4.5 + 3 × v₁

19.5 = 5 × v₁

or

v₁ = 3.9 m/s

and

v₂ = 1.5 + v₁

or

v₂ = 1.5 + 3.9

or

v₂ = 5.4 m/s

now,

the loss in the kinetic energy = initial kinetic energy - Final kinetic energy

or

=

or

=

or

the loss in the kinetic energy = 1.05 J

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it