The heart pumps oxygenated blood into arteries and the blood is then circulated around the body.

a) consider a ventricular contraction that accelerates a mass m of blood from rest into an artery oriented in a horizontal direction. to simplify the problem, assume the blood slides along the walls of the artery without friction, like a block of ice on a frozen pond. also assume there are no other forces pushing the blood in the horizontal direction. draw a free body diagram for the blood. label each force with "on" and "by" subscripts.

b) suppose the contraction time is delta t and the final speed of the blood is v. find an expression for the magnitude of the average force applied by the heart on the blood. your answer should be a formula involving the variables m, delta t, and v.

c) reasonably realistic numbers are m= 88 grams, delta t= 0.20s, and v= 4 m/s. what is the value of the magnitude of the force applied by the heart on the blood?

d) now suppose the blood is pumped into the aorta (assumed to be oriented vertically upwards). draw a free body diagram for the blood in case.

e) again, suppose the contraction time is delta t and that the blood starts from rest. this time take the magnitude of the force exerted by the heart on the blood f as a "given". find an expression for the final speed v of the blood in terms of m, delta t, f, and the acceleration of gravity g.

f) use the value you found in part c) for the magnitude of the force applied by the heart on the blood and find the value of the final speed for this vertical acceleration case.