Calculating Average Net Force Experienced by a Gymnast During Landing Phase
What was the average net force experienced by the gymnast during the landing phase?
The average net force experienced by the gymnast during the landing phase is approximately 2341 Newtons.
Impulse-Momentum Principle
The average net force experienced by the gymnast during the landing phase can be calculated using the impulse-momentum principle. This principle states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, it can be expressed as:Impulse = Change in Momentum
To calculate the impulse, we can multiply the average force (F_avg) by the time interval (∆t):Impulse = F_avg * ∆t
The change in momentum (∆p) of the gymnast can be calculated using the equation:∆p = m * ∆v
Where m is the mass of the gymnast and ∆v is the change in velocity. In this scenario, the initial velocity of the gymnast is -9.1 m/s (negative because it is downward) and the final velocity is zero. By calculating the change in velocity:∆v = Final Velocity - Initial Velocity
∆v = 0 m/s - (-9.1 m/s)
∆v = 9.1 m/s
Using the equation for change in momentum, we can determine the impulse:Impulse = m * ∆v
Impulse = 82 kg * 9.1 m/s
Impulse = 749.2 kg·m/s
Finally, we can calculate the average net force experienced by the gymnast by rearranging the impulse formula:Impulse = F_avg * ∆t
749.2 kg·m/s = F_avg * 0.32 s
F_avg = 749.2 kg·m/s / 0.32 s
F_avg ≈ 2341 N