A 6.8 kg block of some unknown material is suspended from a spring scale and submerged in water. The spring scale reads 48.0 N. What is the specific gravity of the block?
To determine the specific gravity of the block, we need to understand the concepts of weight, buoyant force, and specific gravity.
1. Weight: Weight is the force exerted on an object due to gravity. It is given by the formula W = m*g, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
2. Buoyant Force: When an object is submerged in a fluid, it experiences an upward force called the buoyant force. It is given by the formula F_b = V*d*g, where F_b is the buoyant force, V is the volume of the displaced fluid, d is the density of the fluid, and g is the acceleration due to gravity.
3. Specific Gravity: The specific gravity of a substance is the ratio of its density to the density of a reference substance. In the case of liquids, water is commonly used as the reference substance. The specific gravity of an object can be determined using the formula SG = d_object / d_water, where SG is the specific gravity, d_object is the density of the object, and d_water is the density of water.
Now let's apply these concepts to solve the problem:
1. First, calculate the weight of the block using the formula W = m*g:
W = (6.8 kg) * (9.8 m/s^2) = 66.64 N
2. Next, determine the buoyant force that acts on the block when submerged:
F_b = W (since the block is in equilibrium) = 66.64 N
3. The buoyant force on the block is equal to the weight of the fluid displaced by the block. Since the block is submerged in water, the buoyant force is given by the formula F_b = V*d*g, where d is the density of water and g is the acceleration due to gravity.
V = F_b / (d*g)
4. We know the mass of the block, so we can calculate its volume using the formula V = m / d_object.
V = (6.8 kg) / d_object
5. Substituting the expression for V in step 4 into the formula for the buoyant force:
F_b = ((6.8 kg) / d_object) * d * g
6. Equating the expression for F_b from step 5 to the known value of 48.0 N given by the spring scale:
48.0 N = ((6.8 kg) / d_object) * d * g
7. Rearranging the equation to solve for d_object / d:
d_object / d = (48.0 N * d_object) / (6.8 kg * g)
8. Finally, substituting the specific gravity formula into the equation from step 7:
SG = d_object / d = (48.0 N * d_object) / (6.8 kg * g)
By calculating the right side of the equation, you can find the specific gravity of the block.