1. a) A leg is held as shown. The lower leg has a mass of 3.5 kg and its center

Question

1. a) A leg is held as shown. The lower leg has a mass of 3.5 kg and its center of mass is halfway between the knee and foot. There is a tendon force, applied upwards 5.0 cm from the knee. Find the force from the upper leg, magnitude in Newtons and direction, applied at the knee that is needed to keep the leg in equilibrium.

b) How much work, in Joules, is done to bring to a complete stop a boat with a mass of 1300 kg that starts out at a speed of 1.4 m/s?  

c) A ride at a carnival consists of chairs hanging from (massless) chains that are connected to a rigid central structure, as shown. The central structure spins, causing the chairs to move in a circular path. If the structure spins at 16 rev/min (rpm) and each chain is 4.5 meters long, what must be the angle (in degrees) between the chain and vertical?

d) A toy gyroscope is spun up by a string attached at a radial distance of 1.3 cm. If the string is pulled at an acceleration of 0.25 m/s2 for 1.5 seconds, what angular velocity does the gyroscope get?

Explanation / Answer

b] Work = change in KE = - 0.5 mv^2 = -0.5*1300*1.4^2 = -1274 J

c] tan theta = w^2r/g where r is L sin theta.

tan theta = (16*2pi/60)^2*4.5 sin theta/9.8

tan theta = 1.289 sin theta

1/cos theta = 1.289

cos theta = 1/1.289

theta = arccos(1/1.289) = 39.1 degree answer

d] w^2r = a. where r = 1.3 - 0.5*0.25*1.5^2 = 1.019 m

w = sqrt(a/r) = sqrt(0.25/1.019) = 0.495 rad/s answer

a] figure should be given for better idea,

F = mg = 3.5*9.8 = 34.3 N upward

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