Problem 8.45: Changing Your Center of Mass. To keep the calculations fairly simp
ID: 1417988 • Letter: P
Question
Problem 8.45: Changing Your Center of Mass. 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 is 8.50 kg , while that of the lower leg (including the foot) is 5.50 kg . Take the x-axis to be directed horizontally and the y-axis to be directed vertically downward. Part A Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is fully extended along the y axis. Express your answer to three significant figures. yc = 41.1 cm SubmitMy AnswersGive Up All attempts used; correct answer displayed Part B Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is fully extended. Express your answer to the nearest integer. xc = 0 cm SubmitMy AnswersGive Up Correct Part 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 (which is parallel to the ground). Express your answer to three significant figures. xc = cm Part 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 (which is parallel to the ground). Express your answer to three significant figures. yc = cm
Explanation / Answer
a)
set x=0 as the position of the hip joint
xcm = (x1m1 + x2m2) / (m1+m2)
where
x1 = location of mass1;
m1 = mag of mass1
x2 = location of mass 2;
m2 = mag of mass2
x1 = 23 cm; (x1=23 cm since the upper part is 46 cm, and a uniform object has its center of mass at the midpoint )
m1 = 8.5 kg
x2 = 69 cm;
m2 = 5.5 kg
xcm = (23*8.5 + 69*5.5) / (8.5 + 5.5)
xcm = 41.2 cm
b)
x1 is the same in this case, but now x2 = 46 cm since the lower part lies along the line x = 46 cm
xcm = (23*8.5 + 46*5.5) / 14 = 32.03 cm
c)
here, y1 =0 since the upper part lies along the line y = 0
y2 = -23 cm
ycm = (y1m1 + y2m2) / 14
ycm = (0 + (-23)(5.5)) / 14 = -9.03 cm