This study aims to evaluate a grip strength model designed to elucidate the relationship between measured grip force and muscular activity and assess its impact on an upper limb musculoskeletal model. This work aims to develop the grip strength model by utilizing a piecewise linear function based on the Woods and Bigland-Ritchie EMG-force model, which derives its parameters from 10 adult participants performing isometric and dynamic gripping tasks. Experimental results demonstrate the model's efficacy in estimating surface electromyography (sEMG) readings from force measurements, with a mean root mean square error (RMSE) of 0.2035 and a standard deviation of 0.1207. Moreover, incorporating sEMG readings associated with grip force does not significantly affect the optimization of muscle activation in the upper arm, as evidenced by kinematic data analysis from dynamic tasks. This validation underscores the model's potential to enhance musculoskeletal model-based motion analysis pipelines without distorting results. Consequently, this research emphasizes the prospect of integrating external models into existing human motion analysis frameworks, presenting promising implications for physical Human-Robot Interactions (pHRI).