A cubic meter of some material has a mass of 6400 kg. The block of material is lowered into a lake by a strong cable until the block is completely submerged. Draw a free-body diagram for the block. (Do this on paper. Your instructor may ask you to turn in your work.)
Find the buoyant force on the block and the tension in the cable.
FB = N
T = N
weight in air = 6400 * 9.81
volume of water displaced = 1 m^3
weight of water displaced = 1000 *9.81 *1
= 9810 N = force up from water
tension = (6400 - 1000)(9.81)
= 52,974 N
Well, I seem to have lost my ability to draw, but I can certainly help you with the calculations!
The buoyant force on the block can be found using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the submerged object.
Since the block is completely submerged in the lake, it displaces a volume of water equal to its own volume. Given that the block has a volume of 1 cubic meter, we can determine the weight of the fluid displaced using the density of water, which is approximately 1000 kg/m^3.
Weight of the fluid displaced = density of water * volume of fluid displaced
= 1000 kg/m^3 * 1 m^3
= 1000 kg
So the buoyant force exerted on the block is equal to 1000 kg, or 1000 N.
Now, let's consider the tension in the cable. The tension in the cable must be equal to the weight of the block plus the buoyant force, since the block is in equilibrium.
The weight of the block can be determined using its mass and the acceleration due to gravity. Given that the mass of the block is 6400 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the block.
Weight of the block = mass of the block * acceleration due to gravity
= 6400 kg * 9.8 m/s^2
= 62720 N
Adding this to the buoyant force, the tension in the cable is equal to:
Tension in the cable = weight of the block + buoyant force
= 62720 N + 1000 N
= 63720 N
So the tension in the cable is 63720 N.
Hope that helps, and sorry for the lack of drawing!
To draw a free-body diagram for the block, we need to consider all the forces acting on it.
1. Gravitational force (Weight): This force acts vertically downwards and is equal to the mass of the block multiplied by the acceleration due to gravity. In this case, the gravitational force is equal to (mass of the block) * (acceleration due to gravity) = 6400 kg * 9.8 m/s^2 = 62720 N (acting downwards).
2. Buoyant force: This force acts vertically upwards and is equal to the weight of the fluid displaced by the submerged block. The buoyant force is equal to the weight of the water displaced by the block, which in this case is equal to the weight of a cubic meter of water. The weight of a cubic meter of water is equal to (mass of water) * (acceleration due to gravity) = 1000 kg * 9.8 m/s^2 = 9800 N (acting upwards).
3. Tension in the cable: Since the block is being lowered into the lake by a cable, there is tension in the cable. The tension in the cable is equal to the sum of all the forces acting on the block. In this case, the tension in the cable is equal to the gravitational force + the buoyant force = 62720 N + 9800 N = 72520 N (acting upwards).
Therefore, the free-body diagram for the block will have the following forces:
------> FB = 9800 N (buoyant force - acting upwards)
------> T = 72520 N (tension in the cable - acting upwards)
------> Weight = 62720 N (gravitational force - acting downwards)
To find the buoyant force on the block and the tension in the cable, we need to consider the forces acting on the block when it is submerged in the lake.
First, let's draw a free-body diagram for the block:
1. Start by drawing a rectangle to represent the block. Label it as "Block".
2. Add an arrow pointing upwards from the center of the block. Label this arrow as "Buoyant force (FB)".
3. Add another arrow pointing downwards from the center of the block. Label this arrow as "Weight (W)".
4. Finally, draw a diagonal arrow from the top of the block to the point where the cable is attached. Label this arrow as "Tension in the cable (T)".
Now, to find the values of the buoyant force and tension in the cable:
- The weight of the block can be calculated using the formula:
Weight (W) = Mass x Acceleration due to gravity
Given that the mass of the block is 6400 kg and the acceleration due to gravity is approximately 9.8 m/s^2 (standard value), you can calculate the weight of the block.
- The buoyant force on the block is equal to the weight of the water displaced by the block. Since the block is completely submerged, the buoyant force is equal to the weight of the block itself.
- To find the tension in the cable, we need to consider the net force acting vertically on the block. The net force is the difference between the buoyant force and the weight of the block. The tension in the cable should be equal to the net force.
Using these calculations, you can determine the values of the buoyant force (FB) and the tension in the cable (T) on your own.