A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system? (1 point) Responses 12mv2=12kx2 1 half m v squared is equal to 1 half k x squared mgh=kx2 mg h is equal to k x squared mgh=12kx2 mg h is equal to 1 half k x squared 12mv2=kx2

Question

A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system? (1 point) Responses 12mv2=12kx2 1 half m v squared is equal to 1 half k x squared mgh=kx2 mg h is equal to k x squared mgh=12kx2 mg h is equal to 1 half k x squared 12mv2=kx2

Answer 1

1 half m v squared is equal to 1 half k x squared

Answer 2

The correct equation that shows the conservation of mechanical energy for this system is:

1/2 mv^2 + 1/2 kx^2 = mgh

where:
m represents the mass of the marble,
v represents the velocity of the marble,
k represents the spring constant,
x represents the displacement of the spring,
g represents the acceleration due to gravity,
and h represents the height of the marble above a reference point.

Answer 3

To determine the equation that correctly shows the conservation of mechanical energy for this system, we need to understand the concept of mechanical energy and the different forms it can take.

Mechanical energy is the sum of potential energy (PE) and kinetic energy (KE) in a system. In this case, the marble attached to a compressed horizontal spring, we can assume that there is no loss of energy due to friction or other external factors.

When the spring is released, potential energy from the compressed spring is converted into kinetic energy as the marble starts to move. As the marble moves, potential energy decreases while kinetic energy increases, but the total mechanical energy remains constant.

Now let's examine the given equation options:

1) 12mv^2 = 12kx^2
This equation does not accurately represent the conservation of mechanical energy because it includes the factor of 12. Energy is conserved without any coefficient.

2) 1/2mv^2 = 1/2kx^2
This equation is the correct representation of the conservation of mechanical energy. It states that half of the mass (m) times the velocity squared (v^2) is equal to half of the spring constant (k) times the displacement squared (x^2).

So, the correct equation showing the conservation of mechanical energy for this system is:
1/2mv^2 = 1/2kx^2