The density of gold is 19 times that of water. If you take a gold crown weighing 32 N and submerge it in water, how much upward force must you exert on the submerged crown to keep it from accelerating?

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ρ(g)=19•ρ(w).

The buoyance force F =ρ(w) •V•g= =ρ(g)•V•g/19.
The weight of the crown
W = ρ(g)•V•g = 32 N =>
ρ(g)•V•g/19=32/19 =1.68 N.

Upward force =W-F=32 – 1.68 =30.32 N

To determine how much upward force you must exert on the submerged gold crown to keep it from accelerating, we need to consider the buoyant force acting on the crown.

The buoyant force is equal to the weight of the fluid displaced by the submerged object. In this case, the fluid is water.

Step 1: Calculate the weight of the water displaced
To find the weight of the water displaced, we can use the formula:

Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity

Since the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2, we need to determine the volume of water displaced by the gold crown.

Step 2: Calculate the volume of water displaced
The volume of water that the gold crown displaces is equal to its own volume. We can calculate this using the formula:

Volume of gold crown = weight of gold crown / density of gold

Given that the weight of the gold crown is 32 N and the density of gold is 19 times that of water, which means the density of gold is 19000 kg/m^3, we can substitute these values into the formula to find the volume of water displaced.

Step 3: Calculate the buoyant force
Now that we know the volume of water displaced, we can calculate the buoyant force using the formula:

Buoyant force = weight of water displaced * acceleration due to gravity

Substituting the weight of the water displaced and the acceleration due to gravity into the formula, we can find the buoyant force acting on the gold crown.

Step 4: Calculate the upward force required
To keep the submerged gold crown from accelerating, the upward force exerted must be equal to the buoyant force acting on the crown. Therefore, the upward force required is equal to the buoyant force.

By following these steps, you can find out how much upward force has to be exerted on the submerged gold crown to keep it from accelerating.

To determine the upward force required to keep the submerged crown from accelerating, we need to consider the principle of buoyancy.

The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This is known as Archimedes' principle.

Given that the density of gold is 19 times that of water, we can conclude that the crown will displace its own weight in water plus an additional fraction of its weight equal to 18 times the weight of the water displaced.

First, we need to calculate the volume of water displaced by the crown to determine the weight of the water displaced.

The weight of the water displaced is given by the formula: weight = density × volume × acceleration due to gravity.

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².

Let's assume that the volume of the crown is V cubic meters.

Weight of the water displaced = 1000 kg/m³ × V m³ × 9.8 m/s² = 9800 V N.

Since the density of the gold crown is 19 times that of water, the weight of the crown is 32 N.

Now, the total weight of the water displaced by the crown is the sum of the weight of the water and the weight of the crown:

Weight of water displaced + Weight of crown = 9800 V N + 32 N.

According to Archimedes' principle, the upward force required to keep the submerged crown from accelerating is equal to the weight of the water displaced plus the weight of the crown:

Upward force = Weight of water displaced + Weight of crown = 9800 V N + 32 N.

Therefore, to find the upward force required, we need to know the volume of the crown, V.