Final answer:
The mass of the block of wood is calculated based on the given lift force and the known acceleration due to gravity. Since the block is floating and the forces are balanced, the mass comes out to be 3.06 kg.
Step-by-step explanation:
The student is asking about the mass of a block of wood floating in water given that the lift force, or the buoyant force, of the water is 30.0 N. To answer this, we can use the principle of buoyancy, which states that the buoyant force is equal to the weight of the fluid displaced by the object. Since the block is floating motionless, the upward buoyant force must equal the downward force of gravity on the block. The force of gravity is the block's mass times the acceleration due to gravity (g = 9.8 m/s2). Therefore, the equation to find the mass (m) of the block is 30.0 N = m * 9.8 m/s2. Solving for m gives us m = 30.0 N / 9.8 m/s2 = 3.06 kg. Thus, the correct answer is (a) 3.06 kg.