Understanding the mechanical properties of nanoscale systems requires new experimental and theoretical tools. In particular, force sensors compatible with nanomechanical testing experiments and with sensitivity in the nN range are required. Here, we report the development and testing of a tuning-fork-based force sensor for in situ nanomanipulation experiments inside a scanning electron microscope. The sensor uses a very simple design for the electronics and it allows the direct and quantitative force measurement in the 1-100 nN force range. The sensor response is initially calibrated against a nN range force standard, as, for example, a calibrated Atomic Force Microscopy cantilever; subsequently, applied force values can be directly derived using only the electric signals generated by the tuning fork. Using a homemade nanomanipulator, the quantitative force sensor has been used to analyze the mechanical deformation of multi-walled carbon nanotube bundles, where we analyzed forces in the 5-40 nN range, measured with an error bar of a few nN.