A 2 kg brick falls at 5.1 m/s from a height of 6 m above a spring that has a spring constant of 47 N/m. The brick strikes and compresses the spring until it stops moving. Ignore friction effects.

How much is the spring compressed by the brick?
Assume that there is no Eg after the brick comes into contact with the spring.

To find the compression of the spring, we can use the concept of conservation of energy.

The potential energy of the brick before it falls is given by the formula:
Potential energy (PE) = mass (m) * gravity (g) * height (h)

PE = 2 kg * 9.8 m/s^2 * 6 m
PE = 117.6 J

When the brick hits the spring, the potential energy gets converted into elastic potential energy stored in the compressed spring.

The formula for elastic potential energy is:
Elastic potential energy (PEelastic) = (1/2) * spring constant (k) * (compression distance)^2

Since we want to find the compression distance, we can rearrange the equation as follows:
Compression distance (x) = sqrt(2 * PEelastic / k)

Plugging in the values:
x = sqrt(2 * 117.6 J / 47 N/m)
x ≈ 0.877 m

Therefore, the spring is compressed by approximately 0.877 meters when the brick stops moving.

To find out how much the spring is compressed by the brick, we can use the principle of conservation of mechanical energy. The initial potential energy of the brick (mgh) is converted into the potential energy stored in the compressed spring (½kx²), where m is the mass of the brick, g is the acceleration due to gravity, h is the initial height of the brick, k is the spring constant, and x is the compression of the spring.

First, let's calculate the initial potential energy of the brick:
Initial Potential Energy = m * g * h
= 2 kg * 9.8 m/s² * 6 m
= 117.6 Joules

Next, we can calculate the potential energy stored in the compressed spring when the brick comes to a stop:
Potential Energy stored in the spring = ½ * k * x²

Since the brick comes to a stop, its final kinetic energy is zero. Therefore, all the initial potential energy is converted into the potential energy stored in the spring.

Setting the initial potential energy equal to the potential energy stored in the spring, we can solve for x:

117.6 J = ½ * 47 N/m * x²

Now, let's solve for x:

x² = (2 * 117.6 J) / (47 N/m)
x² = 4.8 m²

Taking the square root of both sides:

x = √(4.8 m²)
x ≈ 2.19 m

Therefore, the spring is compressed by approximately 2.19 meters when the brick comes to a stop.