Question

A man whose mass is 68 kg and a woman whose mass is 53 kg sit at opposite ends of a canoe 4 m long, whose mass is 25 kg. (a) relative to the man, where is the center of mass of the system consisting of man, woman, and canoe? (

Answer 1

The center of mass of the system consisting of a man, a woman, and a canoe is approximately 1.79 meters away from the man towards the woman when the man is taken as the reference point.

Step-by-step explanation:

To find the center of mass of the system consisting of a man, a woman, and a canoe, we can use the concept of center of mass for a system of particles. The center of mass (COM) is the point where the total mass of the system can theoretically be concentrated without changing the system's response to external forces. Each person and the canoe can be considered as point masses for this purpose, and we will assume they are positioned along a straight line, with the man and the woman sitting at opposite ends of the canoe.

The position of the COM is given by the following formula:

(m1 * x1 + m2 * x2 + ... + mn * xn) / (m1 + m2 + ... + mn)

Here, (m1, m2, ..., mn) are the masses and (x1, x2, ..., xn) are their respective positions from a reference point. For simplicity, let's choose the position of the man as the reference point and assume he is sitting at the zero position on the canoe.

We can calculate it as:

(68 kg * 0 m + 53 kg * 4 m + 25 kg * 2 m) / (68 kg + 53 kg + 25 kg) which simplifies to ((0 + 212 + 50) / (146 kg) = 262 / 146 ≈ 1.79 m. Therefore, the center of mass of the system, relative to the man, is approximately 1.79 meters away from him towards the woman.