For the purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass = 40.4 kg) with a center of mass located on the y axis at a point 0.403 m above the origin, (2) the upper legs (mass = 15.2 kg) with a center of mass located on the x axis at a point 0.158 m to the right of the origin, and (3) the lower legs and feet (total mass = 9.49 kg) with a center of mass located 0.480 to the right of and 0.210 m below the origin. Find the (a) x coordinate and (b) the y coordinate of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the whole-body mass) has been ignored to simplify the drawing.

m1 = 40.4 x1 = 0.00 y1 = .403

m2 = 15.2 x2 = .158 y2 = 0.00
m3 = 9.49 x3 = 0.48 y3 = -.210

m = 65.09 kg

x cg = [40.4*0+15.2*.158+9.49*.48]/65.09
= 0.107 m

y cg =[40.4*.403+15.2*0+9.49*-.21]/65.09
= 0.22 m

To find the center of mass of the human figure, you need to use the principles of weighted averages.

(a) The x-coordinate of the center of mass is calculated by taking the weighted average of the x-coordinates of the three parts of the figure.
Given that the x-coordinate of the torso, neck, and head is 0 (on the y-axis), the x-coordinate of the upper legs is 0.158 m (to the right of the origin), and the x-coordinate of the lower legs and feet is 0.480 m (to the right of the origin), we can calculate the x-coordinate of the center of mass as follows:

x-coordinate of the center of mass = [(mass of torso) * (x-coordinate of torso) + (mass of upper legs) * (x-coordinate of upper legs) + (mass of lower legs and feet) * (x-coordinate of lower legs and feet)] / Total mass

Total mass = mass of torso + mass of upper legs + mass of lower legs and feet
= 40.4 kg + 15.2 kg + 9.49 kg

After substituting the given values, we get:

x-coordinate of the center of mass = [(40.4 kg) * 0 + (15.2 kg) * 0.158 m + (9.49 kg) * 0.480 m] / (40.4 kg + 15.2 kg + 9.49 kg)

Calculate the value on the right-hand side of the equation to find the x-coordinate of the center of mass.

(b) The y-coordinate of the center of mass is calculated by taking the weighted average of the y-coordinates of the three parts of the figure.
Given that the y-coordinate of the torso, neck, and head is 0.403 m above the origin, the y-coordinate of the upper legs is 0, and the y-coordinate of the lower legs and feet is 0.210 m below the origin, we can calculate the y-coordinate of the center of mass as follows:

y-coordinate of the center of mass = [(mass of torso) * (y-coordinate of torso) + (mass of upper legs) * (y-coordinate of upper legs) + (mass of lower legs and feet) * (y-coordinate of lower legs and feet)] / Total mass

After substituting the given values, we get:

y-coordinate of the center of mass = [(40.4 kg) * 0.403 m + (15.2 kg) * 0 + (9.49 kg) * (-0.210 m)] / (40.4 kg + 15.2 kg + 9.49 kg)

Calculate the value on the right-hand side of the equation to find the y-coordinate of the center of mass.

To find the x and y coordinates of the center of mass of the human figure, we can use the principle of the center of mass. The center of mass of an object or system is the point at which the total mass of the system can be considered to be concentrated.

(a) To find the x-coordinate of the center of mass, we need to calculate the weighted average of the x-coordinates of the three parts of the figure, based on their masses.

The formula for the x-coordinate of the center of mass is given by:
x_com = (m1*x1 + m2*x2 + m3*x3) / (m1 + m2 + m3)

Let's substitute the values given:
m1 = 40.4 kg (mass of torso, neck, and head)
x1 = 0 (since the center of mass is on the y-axis)
m2 = 15.2 kg (mass of upper legs)
x2 = 0.158 m (x-coordinate of the center of mass of upper legs)
m3 = 9.49 kg (mass of lower legs and feet)
x3 = 0.480 m (x-coordinate of the center of mass of lower legs and feet)

Using the formula, we have:
x_com = (40.4*0 + 15.2*0.158 + 9.49*0.480) / (40.4 + 15.2 + 9.49)

Calculating this expression gives us the x-coordinate of the center of mass.

(b) To find the y-coordinate of the center of mass, we use the same approach as before, but now calculating the weighted average of the y-coordinates of the three parts of the figure.

The formula for the y-coordinate of the center of mass is given by:
y_com = (m1*y1 + m2*y2 + m3*y3) / (m1 + m2 + m3)

Let's substitute the values given:
m1 = 40.4 kg (mass of torso, neck, and head)
y1 = 0.403 m (y-coordinate of the center of mass of torso, neck, and head)
m2 = 15.2 kg (mass of upper legs)
y2 = 0 (since the center of mass is on the x-axis)
m3 = 9.49 kg (mass of lower legs and feet)
y3 = -0.210 m (y-coordinate of the center of mass of lower legs and feet)

Using the formula, we have:
y_com = (40.4*0.403 + 15.2*0 + 9.49*(-0.210)) / (40.4 + 15.2 + 9.49)

Calculating this expression gives us the y-coordinate of the center of mass.

By solving these equations, we can determine the x and y coordinates of the center of mass of the human figure.