Raft is 4.2m wide and 6.4m long. when horse is loaded onto raft, the raft sinks 3 cm deeper into the water. Find the weight of the horse.
Horse's weight = (additional displaced water volume) * density of water) * g
The additional displaced water is
delta V = (raft area)*0.030 m
W = (4.2)*(6.4)*(0.03)*1000*9.8 newtons
To find the weight of the horse, we need to use the concept of buoyancy. The buoyant force is equal to the weight of the displaced water, which is equal to the weight of the horse. We can use the given information about the sinking of the raft to calculate the displacement volume.
1. We know that the original dimensions of the raft are 4.2m wide and 6.4m long.
2. When the horse is loaded onto the raft, it sinks 3 cm deeper into the water. We need to convert this sinking depth into meters.
- 1 cm = 0.01 m (1 meter is equal to 100 centimeters)
- 3 cm = 0.03 m (3 centimeters is equal to 0.03 meters)
3. Now we need to find the displacement volume of the raft when the horse is loaded onto it.
- Displacement volume = height x width x length
- The height is the sinking depth, which is 0.03 m.
- The width is 4.2 m, and the length is 6.4 m.
- Displacement volume = 0.03 m x 4.2 m x 6.4 m = 0.8064 m^3
4. Finally, the weight of the horse is equal to the weight of the displaced water, which is the same as the displacement volume.
- Weight of the horse = 0.8064 m^3
Therefore, the weight of the horse is 0.8064 cubic meters.