Question

A man whose mass is 72 kg and a woman whose mass is 55 kg sit at opposite ends of a canoe 6 m long, whose mass is 23 kg. (a) relative to the man, where is the center of mass of the system consisting of man, woman, and canoe? (hint: choose a specific coordinate system with a specific origin.) distance from man to center of mass

Answer 1

Answer: We can find the center of mass of the system by using the formula:

x_cm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)

where x_cm is the position of the center of mass, m1, m2, and m3 are the masses of the man, woman, and canoe, respectively, and x1, x2, and x3 are their respective positions relative to an origin we choose.

Let's choose the origin to be at the man's position. Then the woman is at a distance of 6 m from the origin. To find the position of the canoe's center of mass, we need to know where the canoe's center of mass is located relative to the origin. Let's assume that the canoe's center of mass is at its geometrical center, which is at a distance of 3 m from each end.

Using these values, we can calculate the position of the center of mass of the system relative to the man:

x_cm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)

x_cm = (72 kg)(0 m) + (55 kg)(6 m) + (23 kg)(3 m)/(72 kg + 55 kg + 23 kg)

x_cm = 333/50 ≈ 6.66 m

Therefore, the center of mass of the system is 6.66 m from the man's position.