A student in an undergraduate physics lab is studying Archimede\'s principle of
ID: 1505861 • Letter: A
Question
A student in an undergraduate physics lab is studying Archimede's principle of bouyancy. The student is given a brass cylinder and using a triple beam balance finds the mass to be 1.25 kg. The density of this particular alloy of brass is 8.32 g/cm^3. The student ties a massless string to one end of the cylinder and submerges it into a tank of water where there is an apparent reduction in the weight of the cylinder. With this information, calculate the volume of the cylinder and the tension in the string when it was submerged in the tank of water. The density of water is 1.00 g/cm^3 and the acceleration due to gravity is g = 9.81 m/s^2.Explanation / Answer
The brass cylinder has 3 vertical forces. The tension and the buoyant force are the upward forces. Its weight is the downward force. Since the cylinder is not moving, the net force is 0 N
T + Bf – W = 0
T = W – Bf
Weight = 1.74 * 9.81 = 17.0694 N
T = 17.0694 – Bf
To solve this problem, you need to remember the buoyant force is equal to the weight of the displaced water. Since the cylinder is submerged, the volume of the displaced water is equal to the volume of the cylinder.
Buoyant force = Density of water in kg/m^3 * g * Volume of displaced water in m^3
Density of water in kg/m^3 = 1000
Buoyant force = 9810 * Volume of displaced water in m^3
Since we know it mass and density of the cylinder, let’s determine its volume.
Since the density is in g/cm^3 and the mass is in kg, let’s convert the mass to grams.
Mass = 1,740 grams
D = m/V, 8.2 = 1,740/V, V = 1,740/8.2
This is approximately 212 cm^3.
Let’s convert cubic centimeters to cubic meters. 1cm^3= 1 * 10^-6 m^3
To convert multiply by 1* 10^-6.
V = (1,740/8.2) * 10^-6
This is approximately 2.12 * 10^-4 m^3
This is the volume of the cylinder and displaced water. So, we can determine the buoyant force.
Buoyant force = 9810 * (1,740/8.2) * 10^-6
This is approximately 2.08 N.
T = 17.0694 – 9810 * (1,740/8.2) * 10^-6 = 15.52776585 N
This is approximately 15.53 N.
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