A ship anchor made of steel has a weight of 100.5 kN. The steel density of 7.82g/cm^3 and the ship is floating in fresh water of density 1.0 g/cm^3. Calculate the weight of the water displaced, the volume of displace water and the apparent weight of anchor.
I am stuck and i need help on this question. Should i convert the steel weight 100.5 kN to Kg or N ?? Can someone show me how to do it? Its so confusing. Any other tips will be appeciated.
I am stuck and i need help on this question. Should i convert the steel weight 100.5 kN to Kg or N ?? Can someone show me how to do it? Its so confusing. Any other tips will be appeciated.
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(100,500 / 9.8) = 10,255kg.
Density is 7,820kg/m^3.
Volume of anchor = (10,255/7,820) = 1.3114m^3. That's also water volume displaced, of course.
Water density is 1,000kg/m^3.
Weight of water displaced = (1.3114 x 1,000) x 9.8 = 12,852N., or 12.852kN.
Apparent weight = (10,255 - 1,311.4) x 9.8 = 87,647N., or 87.647kN.
Density is 7,820kg/m^3.
Volume of anchor = (10,255/7,820) = 1.3114m^3. That's also water volume displaced, of course.
Water density is 1,000kg/m^3.
Weight of water displaced = (1.3114 x 1,000) x 9.8 = 12,852N., or 12.852kN.
Apparent weight = (10,255 - 1,311.4) x 9.8 = 87,647N., or 87.647kN.
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Apparent weight = Actual weight – Buoyant force
The buoyant force is equal to the weight of the displaced water. Weight = mass * 9.8
Buoyant force = mass of displace water * 9.8
Mass = Density * Volume
Buoyant force = Density of water * Volume of displace water * 9.8
Since the density of the anchor is greater than the density of the water, the entire anchor is under the surface of the water. So, the volume of the displaced water is equal to the volume of the anchor.
Density = Mass ÷ Volume
Volume = Mass ÷ Density
Mass in kg = Weight in N ÷ 9.8, Weight in N = 100,500
Mass in kg = 100,500 ÷ 9.8 = 10,255.1 kg
Since the mass is in kilograms, let’s convert the density to kg/m^3
1 kg = 1000 g, 1 m = 100 cm, 1 m^3 = 1 * 10^6 cm^3
7.82g/cm^3 * 1 kg/1000 g * 1 m^3/ 1 * 10^6 cm^3 = 7,820 kg/m^3
This is the density of steel.
Volume = (100,500 ÷ 9.8) ÷ 7,820 = 1.3114 m^3
This is the volume of the anchor. So this is the volume of the displaced water.
Buoyant force = 1000 * (100,500 ÷ 9.8) ÷ 7,820 * 9.8 = 12,851.6624 N
Apparent weight = 100,500 – Buoyant force
The apparent weight is approximately 87,648 N
The buoyant force is equal to the weight of the displaced water. Weight = mass * 9.8
Buoyant force = mass of displace water * 9.8
Mass = Density * Volume
Buoyant force = Density of water * Volume of displace water * 9.8
Since the density of the anchor is greater than the density of the water, the entire anchor is under the surface of the water. So, the volume of the displaced water is equal to the volume of the anchor.
Density = Mass ÷ Volume
Volume = Mass ÷ Density
Mass in kg = Weight in N ÷ 9.8, Weight in N = 100,500
Mass in kg = 100,500 ÷ 9.8 = 10,255.1 kg
Since the mass is in kilograms, let’s convert the density to kg/m^3
1 kg = 1000 g, 1 m = 100 cm, 1 m^3 = 1 * 10^6 cm^3
7.82g/cm^3 * 1 kg/1000 g * 1 m^3/ 1 * 10^6 cm^3 = 7,820 kg/m^3
This is the density of steel.
Volume = (100,500 ÷ 9.8) ÷ 7,820 = 1.3114 m^3
This is the volume of the anchor. So this is the volume of the displaced water.
Buoyant force = 1000 * (100,500 ÷ 9.8) ÷ 7,820 * 9.8 = 12,851.6624 N
Apparent weight = 100,500 – Buoyant force
The apparent weight is approximately 87,648 N
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You're on the right track. This is an exercise in unit conversions, which can be a pain. The weight was given in kN because weight requires gravity. Divide by 9.81 and multiply by 1000 to get the mass in kg, Multiply by 1000 again to get the mass in grams, then divide by 7.82 to get cm^3 and multiply by 1 g/cm^3 to get mass of water. And, you can do the conversions in a different order if you want. It often helps to write the units on each number so you can watch that they cancel properly during division and multiply properly during multiplication.
I used wiki.answers to get the conversion numbers.
I used wiki.answers to get the conversion numbers.