A metal block of mass 1.840 kg is hanging from a string. The tension in the string is 9.972 N. The block is submerged in a beaker of fluid and is stationary. What is the magnitude and direction of the buoyant force acting on the block? Consider making a free body diagram showing the three forces acting on the block.
I know the formula is F=PA but I'm confused on the steps to take. Please help!
The difference between the mg and tension force is the buoyant force.
Thank you so much!
To find the magnitude and direction of the buoyant force acting on the block, we need to consider the forces acting on it and use the principles of buoyancy.
First, let's draw a free-body diagram showing the three forces acting on the block:
1. The weight of the block: This is the force due to gravity acting on the block and can be calculated using the formula weight = mass × 9.8 m/s².
Given that the mass of the block is 1.840 kg, the weight can be calculated as weight = 1.840 kg × 9.8 m/s² = 18.032 N. The weight acts downward.
2. The tension in the string: The tension in the string is given as 9.972 N and acts upward since it is supporting the weight of the block.
3. The buoyant force: This is the force exerted by the fluid on the block and acts in the opposite direction of the weight. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the block.
To find the magnitude of the buoyant force, we need to know the density of the fluid and the volume of the block. Unfortunately, that information is not given in the question. So, we cannot determine the magnitude of the buoyant force without additional data.
However, we can determine the direction of the buoyant force. Since the block is stationary, the magnitude of the buoyant force must be equal to the magnitude of the weight of the block, but in the opposite direction. Therefore, the direction of the buoyant force is upward.
In summary, without the specific information about the density of the fluid and the volume of the block, we cannot determine the magnitude of the buoyant force. However, we know that its direction is upward.