The density of gold is 19 times that of water. If you take a gold crown weighing 24 N and submerge it in water, how much upward force must you exert on the submerged crown to keep it from accelerating?
19 x water weight for same volume MINUS water weight for same volume.
The result is 18 times the weight of the same volume of water, or 18/19 of the weight of the crown.
To find the upward force you need to exert on the submerged gold crown to keep it from accelerating, you need to consider the principle of buoyancy.
Buoyancy is the upward force exerted on an object submerged in a fluid (in this case, water). This force is equal to the weight of the fluid displaced by the object.
First, let's calculate the weight of the water displaced by the gold crown. We know that the weight of the gold crown is 24 N, and the density of gold is 19 times that of water. Since density is defined as mass divided by volume, we can infer that the volume of the gold crown is 1/19th that of the water.
1. Calculate the volume of the gold crown:
Since density = mass/volume,
Volume of gold crown = mass of gold crown / density of gold = 24 N / (19 x density of water)
2. Calculate the weight of the water displaced by the gold crown:
Weight of water displaced = density of water x volume of gold crown x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s².
Once you have the weight of the water displaced, this is also the buoyant force acting on the gold crown. To keep the crown from accelerating, you need to exert an upward force equal to the buoyant force.
Therefore, the answer to your question is the weight of the water displaced by the gold crown, which can be calculated using the steps above.