Questions: Which equation is appropriate for determining the vertical ground reaction force during the stance phase of running? Fw=mg Fz=mg+a Fz=Fw Fz=m(az-g)

Which equation is appropriate for determining the vertical ground reaction force during the stance phase of running? Fw=mg Fz=mg+a Fz=Fw Fz=m(az-g)

Transcript text: Which equation is appropriate for determining the vertical ground reaction force during the stance phase of running? $F_{w}=m g$ $F_{z}=m g+a$ $F_{z}=F_{w}$ $\mathrm{F}_{\mathrm{z}}=\mathrm{m}\left(\mathrm{a}_{\mathrm{z}}-\mathrm{g}\right)$

Solution

Solution Steps

Step 1: Understanding the Context

The question asks for the appropriate equation to determine the vertical ground reaction force during the stance phase of running. The stance phase is when the foot is in contact with the ground, and the vertical ground reaction force is the force exerted by the ground on the body in the vertical direction.

Step 2: Analyzing the Equations

Let's analyze each given equation:

$ F_{w} = mg $: This equation represents the weight of the body, where $ m $ is mass and $ g $ is the acceleration due to gravity. It does not account for any additional forces during running.
$ F_{z} = mg + a $: This equation seems incorrect as it adds a constant $ a $ to the weight, which doesn't make sense in the context of forces.
$ F_{z} = F_{w} $: This equation states that the vertical ground reaction force equals the weight, which is not always true during dynamic activities like running.
$ F_{z} = m(a_{z} - g) $: This equation accounts for the net acceleration in the vertical direction ($ a_{z} $) minus the gravitational acceleration ($ g $). This is appropriate for dynamic situations like running, where the net force is the product of mass and net acceleration.

Step 3: Selecting the Appropriate Equation

The correct equation should account for the dynamic nature of running, where the vertical ground reaction force is influenced by both gravitational and additional accelerations. The equation $ F_{z} = m(a_{z} - g) $ correctly represents this scenario, as it considers the net vertical acceleration.