The equation for the length of an object as a function of temperature and force depends on the material properties of the object. In general, the relationship between temperature, force, and length can be described by the coefficient of linear expansion and the modulus of elasticity of the material.
The equation that relates the change in length (ΔL) of an object to temperature change (ΔT) and applied force (F) is given by:
ΔL = α * L0 * ΔT + (F / A) * L0 / E
where: ΔL is the change in length of the object, L0 is the initial length of the object, ΔT is the change in temperature, α is the coefficient of linear expansion, F is the applied force, A is the cross-sectional area of the object, and E is the modulus of elasticity of the material.
The coefficient of linear expansion (α) represents how much the length of the material changes per unit change in temperature. The modulus of elasticity (E) represents the material's resistance to deformation under an applied force.
It's important to note that this equation assumes a linear relationship between length, temperature, and force, and it may not be applicable to all materials or situations. Different materials have different temperature and force dependencies, and more complex equations or material-specific equations may be required for accurate calculations.