A 38-kg plastic ocean kayak has a sealed interior filled with air (like a big, h
ID: 2098543 • Letter: A
Question
A 38-kg plastic ocean kayak has a sealed interior filled with air (like a big, hard-plastic balloon), so that the paddler basically sits on top of the floating kayak. The kayak has a total volume of 0.46m^3. (Assume p_seawater = 1025 kg/m^3)
a. While the kayak is floating on water, what mass of water does it displace?
b. While the kayak is floating on water, what volume of water does it displace?
c. While the kayak is floating on water, what is the magnitude of the NET force acting on it?
d. Suppose now that you can completely submerge the kayak underwater (something that would take tremendous effort), and then release it. What will be the magnitude and direction of the acceleration of the kayak immediately after you release it?
Explanation / Answer
p* V*g = mg => 1025 * V = 38 => V = 0.034 m^3 a). mass of water displaced = 0.034 * 1025= 34.85 kg b). volume= 0.034 m^3 c). net force acting = p* V* g = 1025 * 0.034 *9.8 =341.53 N in the upward direction d). acceleration = [1025 * 0.46 *9.8 - 38 * 9.8]/38 => a= 111.8 m/s^2 in the upward direction