cal pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is

Question

cal pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable. Calculate the kinetic energy that the earth has because of (a) its rotation about its own axis and (b) its motion around the sun. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 1.1 X 102OJ. ssm Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.00 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 6.00 kg and r1 = 2.00 m, (2) m2 = 4.00 kg and r2 = 1.50 m, (3) m3 = 3.00 kg and r4 = 3.00 m. (a) Find the tangential speed of each object.

Explanation / Answer

t1=24 h=86400 s w1=2*pi/t1=7.26*10^-5 rad/s I=(2/5)*m*R^2=9.73*10^37 kg m^2 a)about its own axis=0.5*I*w1^2=2.56*10^29 j b)t2=365 days=31536000 s w2=1.99*10^-7 rad/s distance between sun and earth=d=1496*10^8m v2=w2*d=29790.96 m/s ke=0.5*m*v2^2+0.5*I*w1^2=2.65*10^33 j

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