Question

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?

Answer 1

Answer:

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)

Data:

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 data:

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

F*(0.0197) =24.141

F= (24.141)/(0.0197)

F= 1225.43 N