A boat having a length 5 m and width 4 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is _________ Kg.
Question
A boat having a length 5 m and width 4 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is _________ Kg.
Solution
To find the mass of the man, we need to use the principle of buoyancy, which states that the weight of the water displaced by an object is equal to the weight of the object.
Step 1: Calculate the volume of water displaced The boat sinks by 1 cm when the man gets on it. This means that the volume of the water displaced is equal to the volume of the boat that is submerged when the man is on it.
The volume (V) of a rectangular prism (like the submerged part of the boat) is calculated by multiplying the length (L), width (W), and height (H). In this case, the length and width of the boat are 5 m and 4 m respectively, and the height is the amount the boat sinks, which is 1 cm or 0.01 m.
So, V = L * W * H = 5 m * 4 m * 0.01 m = 0.2 cubic meters.
Step 2: Calculate the weight of the water displaced The weight (W) of an object is calculated by multiplying its volume (V) by the density (D) of the material it's made of, and by the acceleration due to gravity (g).
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.
So, W = V * D * g = 0.2 m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 1960 N.
Step 3: Convert the weight to mass The weight of an object is related to its mass (m) by the equation W = m * g. Therefore, we can find the mass of the man by rearranging this equation to m = W / g.
So, m = 1960 N / 9.8 m/s^2 = 200 kg.
Therefore, the mass of the man is 200 kg.
Similar Questions
A small ferryboat is 3.90 m wide and 5.70 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.30 cm into the river. What is the weight of the truck? kN
A 49.0 kg person is standing in a canoe while it moves forward at a constant speed of 7.40 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.20 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 12.5 m/s. What is the mass of the canoe? 59.6 kg 21.2 kg 11.5 kg 4.70 kg
A 90.0 kg person is sitting in a 100 kg boat, which is floating at rest on a lake. In the boat is a stone with a mass of 5.00 kg. The person throws the stone at 4.00 m/s horizontally in the NORTH direction. The kinetic energy of the boat and person after throwing the stone is
90. The boat will sink when the weight on it increases beyond 350 kg. There is a hole in it through whichthe water leaks in at the rate of 0.4 kg/s. The weight of the boat is 1200 kg, and the weight of theboatman is 48 kg. The boatman throws out water at the rate of 0.04 kg/s. There are four passengerswhose weights are 42.5 kg, 53.5 kg, 43.5 kg and 54.5 kg. How long will the boat float?(a) 60 hours (b) 80 hours (c) 96 hours (d) 100 hours (e) 120 hours
In a boat, 25 persons were sitting. Their average weight increased by one kilogram when one man leaves and a new man comes in. The weight of the new man is 70 kgs. Find the Weight of the man who has left.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.