Atoms, Protons, Neutrons, and Electrons
Setting reference frame so that the x axis is along the incline and y is perpendicular to the incline
<span>X: mgsin65 - F = mAx </span>
<span>Y: N - mgcos65 = 0 (N is the normal force on the incline) N = mgcos65 (which we knew) </span>
<span>Moment about center of mass: </span>
<span>Fr = Iα </span>
<span>Now Ax = rα </span>
<span>and F = umgcos65 </span>
<span>mgsin65 - umgcos65 = mrα -------------> gsin65 - ugcos65 = rα (this is the X equation m's cancel) </span>
<span>umgcos65(r) = 0.4mr^2(α) -----------> ugcos65(r) = 0.4r(rα) (This is the moment equation m's cancel) </span>
<span>ugcos65(r) = 0.4r(gsin65 - ugcos65) ( moment equation subbing in X equation for rα) </span>
<span>ugcos65 = 0.4(gsin65 - ugcos65) </span>
<span>1.4ugcos65 = 0.4gsin65 </span>
<span>1.4ucos65 = 0.4sin65 </span>
<span>u = 0.4sin65/1.4cos65 </span>
<span>u = 0.613 </span>
Answer: P = 36.75W
The additional power needed to account for the loss is 36.75W.
Explanation:
Given;
Mass of the runner m= 60 kg
Height of the centre of gravity h= 0.5m
Acceleration due to gravity g= 9.8m/s
The potential energy of the body for each step is;
P.E = mgh
P.E = 60 × 9.8 × 0.5
PE = 294J
Since the average loss per compression on the leg is 10%.
Energy loss = 10% (P.E)
E = 10% of 294J
E = 29.4J
To calculate the runner's additional power
given that time per stride is = 0.8s
Power P = Energy/time
P = E/t
P = 29.4J/0.8s
P = 36.75W
