We show that the force F between a conical surface with a polymer attached to its tip and a plane at distances shorter than the radius of gyration R_g of the polymer depends only on the distance r between the two and the temperature T, and is independent of the specific microscopic details of the polymer: F=ck_BT/r, where the dimensionless prefactor c is determined by the universal exponents c=(γ_c-γ_cp)/ν, where ν is the exponent describing N-dependence of R_g, while the γs are exponents characterizing the N-dependence of the number of configurations for a polymer attached to the tip of the cone (c), and for a polymer attached to a contact point between a cone and a plane (cp). We calculate values of the exponents for ideal polymers in space dimensions d=2,3,4, and for polymers in good solvent in d=3, for all possible apex angles of the cone