A 15.0kg block is attached to a very light horizontal spring of force constant 450N/m and is resting on a smooth horizontal table. Suddenly it is struck by a 3.00kg stone traveling horizontally at 8.00m/s to the right, where upon the stone rebounds at 2.00m/s horizontally to the left. Required:
Find the maximum distance that the block will compress the spring after the collision.

The maximum distance that the block will compress the spring after the collision is 0.365 m

Explanation:

Given;

mass of block, m₁ = 15.0kg

spring constant, k = 450 N/m

mass of stone, m₂ = 3 kg

initial velocity of the stone, u₂ = 8.00m/s

final velocity of the stone, v₂ = 2.00m/s

initial velocity of the block, u₁ = 0 (since it is resting on a smooth horizontal table)

final velocity of the block after collision, v₁ = ?

First, apply the principle of conservation of linear momentum, to determine the velocity of the block after collision;

let right direction be positive and left direction be negative

m₁u₁ + m₂u₂ = m₁v₁ - m₂v₂

15(0) + 3(8) = 15(v₁) - 3(2)

24 = 15v₁ - 6

24 + 6 = 15v₁

30 = 15v₁

v₁ = 30 / 15

v₁ = 2 m/s to the right

Finally, apply the principle of conservation energy to determine the maximum distance the block will compress the spring;

KE₁ + PE₁ = KE₂ + PE₂

¹/₂m₁u₁² + ¹/₂Kx₁² = ¹/₂m₁v₁² + ¹/₂Kx₂²

where;

u₁ is the initial velocity of the block after collision before compressing the spring, = 2 m/s

x₁ is the initial compression of the spring

v₁ is the final velocity of the block after compressing the spring

x₂ is the maximum distance that the block will compress the spring after the collision

¹/₂(15)(2)² + ¹/₂(450)(0)² = ¹/₂(15)(0)² + ¹/₂(450)x₂²

30 = 225x₂²

x₂² = 30 / 225

x₂² = 0.13333

x₂ = √0.13333

x₂ = 0.365 m

Therefore, the maximum distance that the block will compress the spring after the collision is 0.365 m

what is the question because that is not a question.

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