Question

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 8.35 kg , while that of the lower leg (including the foot) is 5.50 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.

ANSWER: Xc= _________ cm

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

ANSWER: Yc= _________cm

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.

ANSWER: Xc= _________ cm

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.

ANSWER: Yc= _________cm

Answer 1

Answer:

Xc = 64.27 cm, Yc = 0 cm, Xc = 27.73 cm, Yc = 18.27 cm

Explanation:

A human leg is 92 cm long equally divided into two parts (upper leg and lower leg) that is both are 46 cm long

M1 = 8.35 kg

M2 = 5.50 kg

A. Starting from hip joint, when the leg is placed horizontally, the X coordinate of centre of mass will be

Xc = (m1x1 + m2x2) / m1 + m2

Xc = (8.35x46 + 5.50 x 92) / 8.35 + 5.50

( here we took x2 = 92 cm because we are measuring length from the hip joint, that means length at hip joint is 0 and at the foot 92 cm)

Xc = 890.1 / 13.85

Xc = 64.27 cm

B. Yc = (y1m1 + y2m2) / m1 + m2

Yc = (0x8.35 + 0x5.50) / 8.35 + 5.50

( here y1 and y2 are 0 because the leg is placed horizontally that means in X direction so none of the leg component is in Y direction)

Yc = 0 cm

C. Xc = (m1x1 + m2x2) / m1 + m2

Xc = (8.35x46 + 5.50x0) / 8.35 + 5.50

(here x2 is taken 0 because the other half leg is bent vertically that means it is in Y direction so its X component is 0)

Xc = 384.1 / 13.85

Xc = 27.73 cm

D. Yc = (m1y1 + m2y2) / m1 + m2

Yc = (8.35x0 + 5.50x46) / 8.35 + 5.50

(here y1 is zero because the upper leg is in X direction and y2 is taken 46 cm because starting measuring from hip joint 46 cm of length of lower leg is in Y direction)

Yc = 253/13.85

Yc = 18.27 cm