Question

In: Physics

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that...

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0 cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 kg person, the mass of the upper leg would be 8.60 kg , while that of the lower leg (including the foot) would be 5.30 kg . Take that x-axis is directed horizontally and the y-axis is directed vertically downward.

A) Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

B) Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

C) Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal.

D) Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal.

Solutions

Expert Solution

when leg is totally held horizontal

then

length of each leg = 92 / 2 = 46 cm

position of center of mass of upper leg = 46/2 = 23 cm

position of center of mass of lower leg = 46 + (46/2) = 69 cm

so,

the center of mass can be found as

x_cm = 8.6 * 0.23 + 5.30 * 0.69 / 8.6 + 5.3

x_cm = 5.635 / 13.9

x_cm = 0.4053 m or 40.53 cm

----------------------------------------------------------

y_cm = 0

there is no y - component when leg is horizontal

--------------------------------------------------

when leg is bent to form a right angle, we have

position of center of mass of upper leg = 46/2 = 23 cm

position of center of mass of lower leg = 46 + (46/2) = 46 i + 23 j

so,

c.o.m = 8.6 * 23 i + 5.30 * (46 i + 23 j) / 8.6 + 5.3

c.o.m = 197.8 i + 243.8 i + 121.9 j / 13.9

c.o.m = 31.7 i + 8.769 j

so,

x - component = 31.7 cm

----------------------------------------------------------------------------

y - component = 8.769 cm

genius_generous answered 1 year ago

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