The magnitude of the buoyant force acting on the block is 16.58 N, and it acts in the upward direction.
To find the magnitude of the buoyant force acting on the block, we need to consider the concept of buoyancy.
The buoyant force is the upward force exerted on an object immersed in a fluid, and it is equal to the weight of the fluid displaced by the object. In this case, the fluid is water, and the block is floating in it.
To calculate the magnitude of the buoyant force, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
First, we need to find the volume of water displaced by the block. We know that the block is floating stationary, which means the weight of the block is balanced by the tension in the string and the buoyant force. Therefore, the weight of the block is equal to the tension in the string.
Using the formula for weight, W = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can find the weight of the block:
W = m * g = 1.688 kg * 9.8 m/s^2 = 16.58 N
Since the block is floating, the buoyant force must be equal to the weight of the block. Therefore, the magnitude of the buoyant force is also 16.58 N.
Now let's consider the direction of the buoyant force. The buoyant force always acts in the opposite direction to the force of gravity. In this case, since the block is floating and the tension in the string is holding it in place, the buoyant force is acting upward.
Therefore, the magnitude of the buoyant force is 16.58 N, and the direction is upward.
In summary, the magnitude of the buoyant force acting on the block is 16.58 N, and it acts in the upward direction.