a) A meter stick of uniform density has total mass 0.150 kg. The stick is balanc

Question

a) A meter stick of uniform density has total mass 0.150 kg. The stick is balanced at the 30 cm mark with an object suspended by a string tied at the 15 cm mark. What is the mass of the object?

b) Three identical straight rods, each 1 m long, are welded together at there ends at right angles to each other. Setting +x, +y, and +z axes to lie along the rods, at what point (x,y,z) is the center of mass of the three rod system?

c) A wire of uniform density and total length L is bent into thirds to form three sides of a square. How far is the center of mass of the wire from the center of the square?

d) When a wire of uniform density and total length L is bent into an arc representing a fraction of a circle f, how far is the center of mass of the wire C displaced from the midpoint of the wire M along the axis of symmetry of the wire? (Hint: taking the the midpoint as the origin M = 0, C = 0 for f = 0, C = L/(2*pi) for f = 1 where pi = 3.14159....)

Explanation / Answer

a) balamcing moment about mark point ,

20 x 0.150g = mg x 15

m = 0.200 kg

b) x_cm   = 0.50 / 3 = 0.167 m
y_cm = 0.167m

z_cm = 0.167 m

=(0.167 , 0.167, 0.167) m

c) one side = L/3

x_cm = - (L/3)/2 / 3 = -L/18

y-cm = 0   

so distance is L/18

d)

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