Question

While a person is walking, his arms (with typical lengths 70 cm measured from the shoulder joint) swing through approximately a 45 angle in 0.5 s. As a reasonable approximation, we can assume that the arm moves with constant speed during each swing.

a. Find the magnitude of the force that the blood vessel must exert on the drop of blood.

Express your answer using two significant figures.

b.

What force would the blood vessel exert if the arm were not swinging?

Express your answer using two significant figures.

Answer 1

Given

Angular displacement = 45 degree = pi/4 radians

Time = t = 0.5s

Angular velocity = Angular displacement/ time = pi/4*t = pi/(4 x 0.5) = 1.57 radians

Acceleration a = (angular velocity)^2 x Arm length = 1.57^2 x 0.7 = 1.727 m/s^2

(a) Total force while arm is swinging = ma + mg = m (a +g) = 0.70 x10^-3 (1.727 + 9.81) = 8.1 x 10^-3 N

( Here we have assumed mass of drop of blood to be equal to 0.70 x 10^-3 kg)

(b) Force when arm is not swinging = mg = 0.70 x10^-3 (9.81) = 6.9 x 10^-3 N