Canoeist Weight Distribution: How Far Can He Reach Without Getting Wet?

[gtaylorMD]

A 56kg canoeist sits at rest at the back end of a 23kg canoe. The canoe is at rest in still water with its front end about 0.50m from the dock. He realizes that he left his paddle on the dock, so he carefully works his way to the front of the 2.3m long canoe. Is he likely to reach the dock from the front of the canoe (without getting wet)? Explain with some estimates

I am completely confused on this one, I believe he can make it without getting wet but I cannot seem to accurately prove that. Thanks for any help

 

[nickjer]

Sounds like conservation of momentum problem. Which means the center of mass won't move since the initial momentum was zero.

 

[nlightner]

on this

I would approach this problem by first considering the weight distribution of the canoe and the canoeist. The canoeist weighs 56kg and is sitting at the back end of the canoe, which weighs 23kg. This means that the combined weight at the back of the canoe is 79kg. As the canoe is 2.3m long, this results in a weight distribution of 34.3kg per meter at the back end of the canoe.

When the canoeist moves to the front of the canoe, the weight distribution will change. Assuming the canoe is still at rest in still water, the combined weight of the canoe and the canoeist will now be distributed evenly along the length of the canoe. This means that the weight per meter at the front of the canoe will be 79kg/2.3m = 34.3kg/m, the same as at the back.

Now, to determine whether the canoeist can reach the dock without getting wet, we need to consider the buoyancy force acting on the canoe. This buoyancy force is equal to the weight of the water displaced by the canoe. Since the canoe is at rest in still water, the buoyancy force will be equal to the weight of the canoe and the canoeist.

Using some estimates, we can assume that the average density of the canoe and the canoeist is approximately 1000 kg/m^3 (the density of water). This means that the buoyancy force acting on the canoe will be approximately 79kg/m * 1000 kg/m^3 = 79,000 N.

Now, to determine the maximum distance the canoeist can reach without getting wet, we need to consider the torque (or turning force) acting on the canoe due to the weight of the canoeist. This torque is equal to the weight of the canoeist multiplied by the distance from the center of mass of the canoe to the point where the canoeist is reaching.

Assuming the center of mass of the canoe is located at the midpoint of its length, the distance from the center of mass to the front of the canoe is 1.15m. This means that the maximum torque the canoeist can exert without tipping the canoe is 56kg * 1.15m = 64.4 Nm.

To determine the maximum distance the canoeist can reach without getting wet, we can use the equation for torque: torque = force * distance