Balance shoe

Thanks for posting. The shoe you have here appears to be the 15-177 Coil Balance Shoe. I am confident this is the replacement you need but be sure to carefully compare the dimensions below.

Alternate image for 15-177

Given the damage to the metal cam in the shoe, you may also want to check the bottom of the sash to determine whether the pivot bar needs to be replaced or not. If so, I'll just need to see a photo of the pivot bar, remove from the window, to identify the correct replacement.