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. Suppose she produces an angular acceleration of 29.5 rad/s2 and her lower leg has a moment of inertia of 0.65 kg⋅m2 . What is the force exerted by a muscle if its effective perpendicular lever arm is 1.9 m?

Answer 1

Answer:

10.09 N

Explanation:

Analogously to Newton's second law, torque can be defined as:

$\tau=I\alpha$

Here, I is the moment of inertia and $\alpha$ is the angular acceleration. We have:

$\tau=(0.65kg*m^2)(29.5\frac{rad}{s^2})\\\tau=19.18N*m$

Torque is the vector product of the position vector of the point at which the force is applied by the force vector:

$\vec{\tau}=\vec{r}\times \vec{F}$

Since the effective lever arm is perpendicular to the force, the angle between them is $90^\circ$. The magnitud of this vector product is defined as:

$\tau=rFsen\theta$.

Solving for F and replacing the known values:

$F=\frac{\tau}{rsen\theta}\\F=\frac{19.18N*m}{1.9m(sen90^\circ)}\\F=10.09N$