A small boat weighs 1000 Newton.It is floating in water.
1)What is the upthrust on the boat?
2)What is the weight of water displaced by the boat?
3)What volume of water is displaced by the boat?
1) 1000 N
2) 1000 N
3) 1000 N / 9.8 N/L = ? L
To answer these questions, we need to understand the concept of buoyancy. I can help you understand and calculate the answers step by step.
1) The upthrust on the boat is equal to the weight of the water it displaces. According to Archimedes' principle, the upthrust or buoyant force is equal to the weight of the fluid displaced by an object.
2) To calculate the weight of water displaced by the boat, we need to use the formula: weight = mass × gravity. Since weight is given in Newtons, we can rearrange the equation to solve for mass: mass = weight ÷ gravity.
Given: weight of the boat = 1000 Newtons, gravity = 9.8 m/s².
Calculating: mass = 1000 N ÷ 9.8 m/s² = 102.04 kg (rounded to two decimal places).
3) To find the volume of water displaced, we can use the formula: volume = mass ÷ density.
The density of water is approximately 1000 kg/m³ (at room temperature and atmospheric pressure).
Calculating: volume = 102.04 kg ÷ 1000 kg/m³ = 0.10204 m³ (rounded to five decimal places).
Therefore, the answers to the questions are:
1) The upthrust on the boat is 1000 Newtons.
2) The weight of water displaced by the boat is 102.04 kg.
3) The volume of water displaced by the boat is approximately 0.10204 m³.
To answer these questions, we need to use Archimedes' principle, which states that the upthrust or buoyant force experienced by an object submerged in fluid is equal to the weight of the fluid displaced by the object.
1) Upthrust on the boat:
The upthrust on the boat is equal to the weight of the water it displaces. Since we are given that the boat weighs 1000 Newton, the upthrust on the boat should also be 1000 Newton.
2) Weight of water displaced by the boat:
Since the upthrust on the boat is equal to the weight of water displaced by the boat, the weight of water displaced by the boat is also 1000 Newton.
3) Volume of water displaced by the boat:
To find the volume of water displaced by the boat, we can use the principle that the weight of water displaced is equal to the weight of the boat. However, we need to know the density of water to calculate the volume.
The density of water is approximately 1000 kg/m^3 or 1000 g/cm^3. Since the weight of the boat is 1000 Newton, we can convert it to kilograms (1 Newton = 1 kg * m/s^2) to find the volume.
Considering the density of water as 1000 kg/m^3:
Weight of water displaced = Weight of the boat = 1000 N
Density of water = 1000 kg/m^3
Weight of water displaced = Density of water * Volume of water * g
1000 N = 1000 kg/m^3 * Volume of water * 9.8 m/s^2
Simplifying the equation, we get:
Volume of water = 1000 N / (1000 kg/m^3 * 9.8 m/s^2)
Calculating the value, the volume of water displaced by the boat is approximately 0.102 m^3 or 102 liters.