A piece of ice its mass is 2.5 kg and at 0.0 C temperature , it is crawling on the ground with 5.7 m/s , what is the mass of the melted ice , if we know all of the kinetic energy of the ice turn into the internal energy (of the ice ) , that we need 3.3 X 10^5 J to melt 1.0 kg ice ?

Thanks a lot

Heatmelting=KE

m*3.3E5=1/2 *2.5*5.7^2
solve for mass m

But I can't understand that solution , I mean where is it from :(( m*3.3E5= )) ?

We have this main law :

dPE + dkE + dU = 0
but what about the potential energy (dPE) ?

To find the mass of the melted ice, we will first calculate the kinetic energy of the moving ice using the mass and velocity given.

The formula for calculating kinetic energy is:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass of the ice (m) = 2.5 kg
Velocity (v) = 5.7 m/s

Substituting the values into the formula:

Kinetic Energy = (1/2) * 2.5 kg * (5.7 m/s)^2

Next, we'll calculate the kinetic energy of the ice. Since the question states that all of this kinetic energy is converted into internal energy, we can equate this to the amount of energy needed to melt the ice.

Kinetic Energy of the ice = Energy needed to melt the ice

Simplifying the equation:

(1/2) * 2.5 kg * (5.7 m/s)^2 = m * (3.3 x 10^5 J/kg)

Now, let's solve for the mass of the melted ice (m):

m = [(1/2) * 2.5 kg * (5.7 m/s)^2] / (3.3 x 10^5 J/kg)

Calculating the mass:

m = [0.5 * 2.5 kg * (5.7 m/s)^2] / (3.3 x 10^5 J/kg)

m = 0.5 * 2.5 * (5.7)^2 / 3.3 x 10^5

m ≈ 0.0407 kg

Therefore, the mass of the melted ice is approximately 0.0407 kg.