a man holds a bukcet under a tap from which water issues vertically at 10m/s. It takes 10secs to fill the bucket, which holds 10kg of water. What is the apparent loss in weight of the bucket when the tap is turned off?
To find the apparent loss in weight of the bucket, we need to calculate the buoyant force acting on the bucket when it is filled with water. The buoyant force is the upward force exerted by a fluid (in this case, water) on an object submerged or partially submerged in it.
First, let's calculate the volume of water that enters the bucket. We know that the bucket is filled in 10 seconds and the water is issuing vertically at a speed of 10 m/s. Since speed equals distance divided by time, the height of the water column inside the bucket can be calculated as:
Height = Speed × Time
Height = 10 m/s × 10 s
Height = 100 m
Next, we need to calculate the volume of water that fills the bucket. The volume of an object can be calculated by multiplying its height by its base area. Assuming the bucket has a uniform cross-section throughout, the volume of water in the bucket can be calculated as:
Volume = Height × Base Area
Now, we have to determine the base area of the bucket. Unfortunately, the question does not provide enough information to directly calculate the base area. Therefore, we need to make an assumption about the shape or dimensions of the bucket's base in order to proceed.
If we assume that the base of the bucket is a simple circular shape, we can calculate the base area using the formula:
Base Area = π × (Radius)^2
Alternatively, if we assume the base is a different regular shape, we can use the appropriate formula to calculate its area.
Once we have the base area, we can calculate the volume of water:
Volume = Height × Base Area
Now, since the density of water is approximately 1000 kg/m³, we can calculate the mass of water in the bucket using the formula:
Mass = Density × Volume
Finally, to find the apparent loss in weight of the bucket, we need to calculate the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the bucket, which is given by:
Buoyant Force = Mass of Water × Acceleration due to Gravity
The apparent loss in weight of the bucket is the magnitude of the buoyant force.