To solve this problem, we need to calculate the magnitude of the buoyant force acting on the ore sample when it is immersed in water.

Given Data:

1. Weight of the sample in air ($W_{air}$) = $17.5 \, \text{N}$
2. Tension in the cord when immersed in water ($T$) = $11.2 \, \text{N}$
3. Density of water ($\rho_{\text{water}}$) = $1000 \, \text{kg/m}^3$

Approach:

The buoyant force ($F_B$) can be determined using the relationship: $F_B = W_{air} - T$ Here:

• $W_{air}$ is the weight of the sample in air.
• $T$ is the tension in the cord when the sample is fully immersed in water.

Calculation:

$F_B = 17.5 \, \text{N} - 11.2 \, \text{N}$ $F_B = 6.3 \, \text{N}$

Conclusion:

The magnitude of the buoyant force acting on the sample is: $\boxed{6.3 \, \text{N}}$

Would you like a detailed explanation of why this formula works or assistance with the next part?

Related Questions:

1. What is the volume of the ore sample based on the buoyant force?
2. How does Archimedes’ principle explain buoyant force?
3. What would be the tension if the sample were immersed in a liquid with a density of $800 \, \text{kg/m}^3$?
4. How can you determine the density of the ore sample from this information?
5. What would happen to the buoyant force if the liquid were oil instead of water?

Tip:

Remember, buoyant force depends only on the displaced fluid's weight, not the object's material!