Question three

Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released,
the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s,
what is the stored energy in the spring when it is compressed? Asume there is no external force.

momentum is conserved

so the larger mass will have a velocity of 3 m/s

the sum of the kinetic energies of the two masses, is the energy stored in the spring

i want to know the answer first

The total kinetic energy of two masses is equal to the store energy of the spring..

momentum is conserve, therefore 18j+36j=54j

To find the stored energy in the compressed spring, we can use the principle of conservation of mechanical energy.

When the masses are released, the initial potential energy stored in the compressed spring will be converted into kinetic energy as the masses move away from each other. Assuming there is no external force, the mechanical energy of the system remains constant.

The formula for potential energy in a compressed spring is given by:

Potential energy (PE) = (1/2) k x^2

where k is the spring constant and x is the compression or displacement of the spring.

Since the problem does not provide the spring constant (k) or the displacement (x), we need to use the given information to calculate these values.

We know that the initial kinetic energy of the smaller mass (2 kg) is given by:

Kinetic energy (KE) = (1/2) m v^2

where m is the mass (2 kg) and v is the velocity (6 m/s).

Substituting the known values, we get:

KE = (1/2) * 2 * (6^2) = 36 J

Since the mechanical energy of the system is conserved, the initial kinetic energy of the smaller mass is equal to the potential energy in the spring when it is compressed.

Therefore, the stored energy in the spring when it is compressed is 36 Joules.