A raft is 4.5 wide and 6.3 long. When a horse is loaded onto the raft, it sinks 2.7 deeper into the water.
What is the weight of the horse?
weight horse= volume water*densitywter*g
= 4.5*6.3*2.7*1000kg/m^3*9.8N/kg
To find the weight of the horse, we can use the concept of buoyancy. Buoyancy is the upward force exerted by a fluid (in this case, water) on an immersed object. It is equal to the weight of the fluid displaced by the object.
To calculate the weight of the horse, we need to determine the volume of water displaced when the horse is loaded onto the raft.
First, let's determine the initial volume of the raft by multiplying its width (4.5) by its length (6.3):
Initial volume of the raft = 4.5 * 6.3 = 28.35 cubic units (let's assume meters).
When the horse is added to the raft, it sinks 2.7 units deeper into the water. This means that the volume of water displaced by the horse and the raft together is equal to the volume of the raft plus the volume of the submerged portion of the horse.
Now we have two scenarios:
1. Initial scenario (without the horse):
- Volume of water displaced = Initial volume of the raft
2. Scenario with the horse:
- Volume of water displaced = Initial volume of the raft + Volume of the submerged portion of the horse
To find the submerged volume of the horse, we need to multiply the additional depth the raft sinks (2.7 units) by its width (4.5):
Submerged volume of the horse = 2.7 * 4.5 = 12.15 cubic units (let's assume meters).
Adding this submerged volume of the horse to the initial volume of the raft gives us the new volume of water displaced with the horse on the raft.
Volume of water displaced with the horse = Initial volume of the raft + Submerged volume of the horse
Volume of water displaced with the horse = 28.35 + 12.15 = 40.5 cubic units (let's assume meters).
Finally, the weight of the horse is equal to the weight of the water displaced by the horse and the raft together.
Weight of the horse = Volume of water displaced with the horse * Density of water * Acceleration due to gravity
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight of the horse = 40.5 * 1000 * 9.8 = 397,800 Newtons (or approximately 397.8 kgf).
Therefore, the weight of the horse is approximately 397.8 kilograms.