Yes, that is the exact model I have, MacBook Pro 7,1 (Apple Icon > About This Mac > More Info ... > 13-inch, Mid 2010.) You can use this item with the 60 or the 85Watt power adapter. Please note: You'll need the proper tools, this item requires 'surgery' into the transformer cube of your power adapter and soldering skills, easy to do though. I mention this because Peter K. Ring Sr mentioned it had no problem 'plugging in' this part. You don't plug it in, you solder it in to the transformer cube.
You can follow this link: http://www.instructables.com/id/How-to-open-and-replace-the-MagSafe-cord-on-an-App/?ALLSTEPS
this may help you, but if you have any trouble to reassemble you can use the tape to wrap it like mine.
There are many instruction videos and articles on how to replace a magsafe cable. Search for them like this:
Here is one, quite possibly not the best one available: