Heat and phase change: latent heat

[alaa410]

Homework Statement

A 42kg block of ice at 0°C is sliding on a horizontal surface. the initial speed of the ice is 7.3 m/s and the final speed is 3.5m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice. Determine the mass of the ice the melts into water

Homework Equations

Q=mL

The Attempt at a Solution

Q=mL + (1/2v^2 final- 1/2v^2initial)?

 

[haruspex]

Q=mL + (1/2v^2 final- 1/2v^2initial)?

What exactly is Q in that equation?
The right hand side is dimensionally inconsistent. It mixes energy and velocity².

 

[alaa410]

q is heat gained or lost; this is the equation they used in the solution so its got to be right...

 

[alaa410]

except they multiply not add

 

[haruspex]

q is heat gained or lost; this is the equation they used in the solution so its got to be right... except they multiply not add

Not exact enough for Q, and the equation would still be nonsensical.
I suggest that the equations ought to say
KE lost = heat gained by ice = mass melted * latent heat of fusion
So now you just need an expression for the KE lost.