I’m on a boat! (3 pts) You are on a 20 meter long boat, it weights 1000 kg, and

Question

I’m on a boat! (3 pts) You are on a 20 meter long boat, it weights 1000 kg, and you weigh 100 kg. Consider the system of you and the boat together. (Assume the boat slides on the water without friction, the boat’s center of mass is at its center, and your center of mass is the same height as the boat’s center of mass)

a) If you are at one end of the boat, how far from the boat’s center is the system’s center of mass?

b) How far does the system’s center of mass move (with respect to the water) if you walk from one end of the boat to the other?

c) Now consider the system of you, the boat, and the anchor of the boat. The anchor is 100 kg (ignore buoyancy of the anchor and weight of the rope from which it hangs) and is hanging in the water 10 meters directly below the center of the boat. Now you are at one end of the boat, how far is the boat’s center from the center of mass of this system?

Explanation / Answer

Here,

CASE1:If you are at one end of the boat, how far from the boat’s center is the system’s center of mass

Assuming man Standing on left side of boat

m1 = 1000kg
m2 = 100kg
L1 = 0 m
L2 = 10 m

X = Centre of mass = M1 * L1 + M2 * L2 / M1+M2

X= (1000*0+100*10)/(1000+100) = 0.90m

the Centre of mass is 0.90m (from the left side of the boat)

Case 2: If man walk one side to another.

Assuming man walk from left to right

If the man walks to the right side of the boat the centre of mass will be the same distance just from the right side to the centre instead of the left so 0.90 m (from the right side of the boat)

Case 3: Anchor ,man ,and Boat

New centre of mass according to position of boat is

X = 1000*0+10*5/1000+10

X = 0.04m

The new centre of mass is 0.04m from centre of boat

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