A 10.8 kg block of metal is suspended from a scale and immersed in water, as in the figure below. The dimensions of the block are 12.0 cm 10.4 cm 10.4 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water.
(a) What are the forces exerted by the water on the top and bottom of the block? Take P0 = 1.0130 105 N/m2.
Ftop: 243.36 N: Your response differs from the correct answer by more than 10%. Double check your calculations. N
Fbottom: 19115.1168: Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N
(b) What is the reading of the spring scale?
9.50208 N: Your response differs from the correct answer by more than 10%. Double check your calculations. N
All my answers were wrong!
I apologize for the incorrect answers. Let's go through the problem step-by-step to find the correct solutions.
(a) To find the forces exerted by the water on the top and bottom of the block, we need to understand the concept of buoyant force. When an object is submerged in a fluid, it experiences an upward force called the buoyant force. This force is equal to the weight of the fluid displaced by the object.
First, let's find the volume of the block. The dimensions are given as 12.0 cm x 10.4 cm x 10.4 cm, so the volume can be calculated as follows:
Volume = length x width x height
Volume = 12.0 cm x 10.4 cm x 10.4 cm
Volume = 1297.28 cm^3
Next, convert the volume to cubic meters for consistency:
Volume = 1297.28 cm^3 x (1 m / 100 cm)^3
Volume = 0.00129728 m^3
Now, we can calculate the weight of the block using its mass and the acceleration due to gravity. The weight is given by:
Weight = mass x acceleration due to gravity
Weight = 10.8 kg x 9.8 m/s^2
Weight = 105.84 N
To find the force exerted by the water on the top of the block, we need to consider the pressure at that depth. The pressure exerted by a fluid at a certain depth is given by:
Pressure = density x gravity x depth
The density of water is approximately 1000 kg/m^3, and the depth is 5.00 cm, which is equal to 0.05 m. Thus, the pressure at that depth is:
Pressure = 1000 kg/m^3 x 9.8 m/s^2 x 0.05 m
Pressure = 490 Pa
The force exerted by the water on the top of the block is equal to the pressure multiplied by the area. The area can be calculated by multiplying the length and width of the block, which are 12.0 cm and 10.4 cm, respectively:
Area = length x width
Area = 12.0 cm x 10.4 cm
Area = 124.8 cm^2
Converting the area to square meters:
Area = 124.8 cm^2 x (1 m^2 / 10,000 cm^2)
Area = 0.01248 m^2
Now, we can find the force exerted by the water on the top of the block:
Ftop = Pressure x Area
Ftop = 490 Pa x 0.01248 m^2
Ftop = 6.11 N
The force exerted by the water on the bottom of the block is the weight of the block minus the force exerted on the top:
Fbottom = Weight - Ftop
Fbottom = 105.84 N - 6.11 N
Fbottom = 99.73 N
Please note that these values may differ slightly due to rounding errors.
(b) To find the reading on the spring scale, we need to consider the net force acting on the block. The net force is the difference between the force exerted by the water on the top and the weight of the block:
Net force = Ftop - Weight
Net force = 6.11 N - 105.84 N
Net force = -99.73 N
Since the spring scale measures the force in the upward direction, we consider the magnitude of the net force, which is 99.73 N. Thus, the reading on the spring scale is 99.73 N.
Again, I apologize for the previous incorrect answers. Please let me know if you have further questions or if there is anything else I can assist you with.