A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 39 rad/s2 and her lower leg has a moment of inertia of 0.619 kg m2. What is the force exerted by the muscle if its effective perpendicular lever arm is 1.97 cm?

F = 1225.43 N

Explanation:

Newton's second law:

F = ma has the equivalent for rotation:

τ = I * α Formula (1)

where:

τ : It is the torque applied (Nxm)

I : it is the moment of inertia with respect to the axis of rotation (kg*m²)

α : It is angular acceleration. (rad/s²)

dа ta:

I = 0.619 kg*m²

α = 39 rad/s²

d = 1.97 cm = 0.0197 m

Formula of the torque

τ = F*d (N*m) Formula (2)

Calculation of the F

We replace Formula (2) in the formula (1)

τ = I * α

F*d = I * α

We replace dа ta:

F * (0.0197) = (0.619) * (39)

F * (0.0197) = 24.141

F = (24.141) / (0.0197)

F = 1225.43 N