Match head rubbed over a distance

[Tybstar]

Hi, I'm trying to work this problem out and unfortunately my book doesn't have an explanation.

Homework Statement

A match head is rubbed a distance d over a rough surface in order to increase the temperature to its flash point. If the patch head material has a mass m and a specific heat c, which equation represents the average force needed to raise the match head's temperature by $$\Delta$$T?

Homework Equations

The answer is:

$$F=\frac{mc\Delta T}{d}$$

The Attempt at a Solution

Do I simply set specific heat capacity (Q) to W: $$Q=W$$ and get:

$$mc\Delta T=Fd$$

and move d over?

I'm working in a MCAT study book and it doesn't go into detail about the heat capacity equation that it gives me, but I'm trying to understand this a little more fully. Thanks for any help!

 

[kuruman]

Do I simply set specific heat capacity (Q) to W: $$Q=W$$ and get:

$$mc\Delta T=Fd$$

and move d over?

Yes. The answer assumes that all the "work" done by the force of friction F is converted to heat.