a solid aluminum ingot weighs 89N in air a)what is the volume b)the ingot is suspended from a rope and totally immersed in water. what is the tension in the rope(the apparent weight of the ingot in water)?
mass = W/g = 9.08 kg
(a) For the volume, divide the above mass by the density of aluminum, which you should look up.
(b) Apparent weight = Actual weight - buoyancy
= 89 N - (Volume)*(water density)*(g)
To determine the volume of the solid aluminum ingot and the tension in the rope when it is immersed in water, we need to make use of the principle of buoyancy.
a) To find the volume of the aluminum ingot:
According to Archimedes' principle, the buoyant force acting on an object when it is immersed in a fluid is equal to the weight of the fluid displaced by the object.
Since the solid aluminum ingot weighs 89N in air, its weight in the fluid (water) will be reduced by the buoyant force. Therefore, the weight of the water displaced by the ingot is 89N.
Density of water = 1000 kg/m^3 (approximately)
The weight of the water displaced is equal to the volume of the ingot times the density of water times the acceleration due to gravity (9.8 m/s^2). Therefore, we can set up the equation:
Weight of water displaced = Volume of ingot * Density of water * Acceleration due to gravity
89N = Volume of ingot * 1000 kg/m^3 * 9.8 m/s^2
Now, solve for the volume of the ingot:
Volume of ingot = 89N / (1000 kg/m^3 * 9.8 m/s^2)
b) To find the tension in the rope:
When the ingot is suspended from a rope and immersed in water, the tension in the rope is equal to the difference between the weight of the ingot in air and its apparent weight in water.
Apparent weight of the ingot in water = Weight of ingot in air - Weight of water displaced
Weight of ingot in air = 89N (given)
Substitute the value obtained for the volume of the ingot from part a) into the equation to calculate the weight of the water displaced:
Weight of water displaced = Volume of ingot * Density of water * Acceleration due to gravity
Apparent weight of the ingot in water = 89N - (Volume of ingot * 1000 kg/m^3 * 9.8 m/s^2)
Therefore, the tension in the rope (apparent weight of the ingot in water) is equal to the apparent weight of the ingot when immersed in water.
To answer the given questions, we need to use two concepts: buoyancy and Archimedes' principle.
a) To find the volume of the solid aluminum ingot, we can use Archimedes' principle. The principle states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
In this case, the buoyant force acting on the ingot when it is fully immersed in water is equal to the weight of the ingot in air. Therefore, the buoyant force is 89N.
Since aluminum has a density of 2700 kg/m^3, we can use the formula for buoyant force F_buoyant = density * volume * g, where g is the acceleration due to gravity (9.8 m/s^2).
Rearranging the equation, we can solve for volume: volume = F_buoyant / (density * g).
Plugging in the values, the volume = 89N / (2700 kg/m^3 * 9.8 m/s^2). This will give you the volume of the aluminum ingot in cubic meters.
b) The tension in the rope can be calculated by finding the apparent weight of the ingot in water. The apparent weight is the difference between the weight of the ingot in air and the buoyant force acting on it in water.
In this case, the weight of the ingot in air is 89N. We already know that the buoyant force is also 89N (as explained in part a).
Therefore, the tension in the rope (apparent weight of the ingot in water) is given by: tension = weight of ingot in air - buoyant force = 89N - 89N = 0N.
Hence, the tension in the rope when the ingot is fully immersed in water is zero.