In class, we considered a mitral valve leaflet modeled as a rigid bar of length lv that is pinned to the heart wall at one end and to a papillary muscle at the other. the other end of the papillary muscle is pinned near the apex of the heart wall. (a) if p is the net pressure across the valve leaflet, and av is its surface area, compute, as functions of θ, the magnitude of the axial force fp in the papillary muscle and the magnitude of the reaction force fr that acts on the valve at o. (in this calculation, assume that the net blood pressure force fbp acts normal to the valve at the point c, which is located a distance d from point o.) then, if the cross-sectional area of the papillary muscle is given by ap , compute the average normal stress in the muscle σp as a function of θ. (b) the valve closes during the time interval 0 ≤ t ≤ ted and remains closed for ted ≤ t ≤ tes, where ted and tes represent the times of end diastole and end systole, respectively. during this time, assume that the pressure is given by p = 1 kpa, 0 ≤ t ≤ ted 1 + 15 sin π(t − ted) 2(tes − ted) kpa, ted ≤ t ≤ tes and the motion of the valve is described by θ = θ0(1 − t/ted), 0 ≤ t ≤ ted 0, ted ≤ t ≤ tes where θ0 is the angle when the value is fully open. 1 in addition, use the following parameter values: lv = 0.8 cm a = 1 cm b = −5 cm d = 0.3 cm av = 1 cm2 ap = 0.1 cm2 θ0 = 60◦ ted = 0.1 s tes = 0.4 s and plot p, θ, the magnitudes of fp and fr, and σp for 0 ≤ t ≤ tes.