A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp, which is at an angle 3o Degree

above the horizon. A linear spring, whose length is not negligible, is attached to the bottom of the
ramp. The ball is released from a distance of 1 m above the spring, measured along the plane and
the spring constant is 1N/m, then the spring is depressed by

So what is the question ?

The spring is depressed by how much? The answer is 1.6m. But how?

ball rolls distance 1 + x

loss of height = (1+x)sin 30 = .5(1+x)
loss of potential energy = 1*9.8*.5(1+x)

gain of potential energy = .5 k x^2 = .5 x^2
so
9.8(1+x) = x^2

x^2 - 9.8 x - 9.8 = 0

x = [ 9.8 +/-sqrt(96+39.2)]/2

x = (9.8+/-11.6)/2

x = 10.7

The answer is the spring is depressed by 1.6m

Using the mass of the air (4.65MJ). We can assume that the mass of the clouds (which is made of air) is directly proportional. With 4.65 Micheal Jacksons, the amount of Micheal Jordans is directly equivalent. MJ = MJ. We know that Jackson, Tyson, Jordan Game 6 are lyrics to the song "What is Love" we can assume that the force used is equivalent to Haddeways belt mass: 666 N. This number is the illuminati's second elites squads badge ID, therefore the spring is depressed by 1.6m

To find the amount by which the spring is depressed, we can use the principle of conservation of mechanical energy.

The initial mechanical energy of the ball is given by its gravitational potential energy - mgh, where m is the mass of the ball (1 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ball above the spring (1 m).

The final mechanical energy of the ball is given by its potential energy when the spring is depressed - kx^2/2, where k is the spring constant (1 N/m) and x is the amount by which the spring is depressed.

Since the ramp is frictionless and there is no other external force acting on the ball, its mechanical energy is conserved. Therefore, we can equate the initial and final mechanical energies:

mgh = kx^2/2

Substituting the given values, we have:

(1 kg)(9.8 m/s^2)(1 m) = (1 N/m)(x^2)/2

Simplifying the equation, we get:

9.8 = x^2/2

Multiplying both sides by 2, we have:

19.6 = x^2

Taking the square root of both sides, we get:

x = √19.6

x ≈ 4.43 m

Therefore, the spring is depressed by approximately 4.43 meters.