A raft is 4.2 m wide and 6.5 m long and it floats on water (density of water = 1000 kg/m3). When a horse is loaded onto the raft, it sinks an additional 0.027 m deeper into the water. What is the weight of the horse (in N)?
Well, it sounds like that horse really knows how to make a splash! Let's dive into the problem, shall we?
To find the weight of the horse, we need to consider the change in buoyancy caused by its addition to the raft. The change in buoyancy is equal to the weight of the horse, so we just need to find the volume of water displaced by the horse.
The volume of water displaced is given by the formula: V = A * d, where A is the area of the raft and d is the change in depth.
Now let's calculate that:
A = length * width = 6.5 m * 4.2 m = 27.3 m2
d = 0.027 m
V = 27.3 m2 * 0.027 m = 0.7381 m3
Since we're given the density of water (1000 kg/m3), we can find the weight (W) of the horse using the formula: W = V * density * g, where g is the acceleration due to gravity (approximately 9.8 m/s2).
W = 0.7381 m3 * 1000 kg/m3 * 9.8 m/s2
After all the calculations, we find the weight of the horse to be approximately W = 7213.644 N. So that horse sure carries some weight! Hope that helps, and remember, horses aren't always great swimmers, so let's keep them on dry land!
To find the weight of the horse, we need to calculate the buoyant force acting on the raft.
The buoyant force (F_b) is equal to the weight of the water displaced by the submerged part of the raft.
In this case, the additional depth to which the raft sinks, 0.027 m, represents the submerged part. Therefore, the volume of water displaced is given by:
Volume = width * length * depth
= 4.2 m * 6.5 m * 0.027 m
= 0.7371 m^3
Since the density of water is given as 1000 kg/m^3, we can calculate the weight of the water displaced:
Weight = Volume * density
= 0.7371 m^3 * 1000 kg/m^3
= 737.1 kg
This weight is equal to the buoyant force (F_b) acting upwards on the raft.
Now, we can use the concept of equilibrium to find the weight of the horse (W_h).
The weight of the horse will be equal to the combined weight of the raft and the force acting downwards on the raft:
Weight of horse (W_h) = Weight of raft + F_b
Since the weight of the horse is unknown, we can substitute it with (W_h) in the equation:
W_h = Weight of raft + F_b
However, the weight of the raft is not given in the question. So, we cannot determine the weight of the horse with the given information.
To find the weight of the horse, we need to understand the concept of buoyancy and use Archimedes' principle.
Buoyancy is the force exerted by a fluid, in this case water, on an object submerged in it. According to Archimedes' principle, the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Here's how we can find the weight of the horse:
1. Determine the volume of water displaced by the raft with and without the horse:
- When the raft is empty, it displaces a volume of water equal to its own volume: 4.2 m * 6.5 m * 0.027 m = 0.7371 m^3.
- When the horse is loaded onto the raft, it displaces an additional 0.027 m of water.
2. Calculate the total volume of water displaced by the horse:
- The total volume of water displaced by the horse will be the sum of the water displaced by the raft alone and the additional water displaced when the horse is loaded.
- Total volume = 0.7371 m^3 + 0.027 m^3 = 0.7641 m^3.
3. Calculate the weight of water displaced by the horse:
- Weight of water = volume of water displaced * density of water.
- Weight of water = 0.7641 m^3 * 1000 kg/m^3 = 764.1 kg (because 1 N = 1 kg * m/s^2, the weight of water in N will be the same as its mass in kg).
4. The weight of the horse will be equal to the weight of the water displaced:
- Therefore, the weight of the horse is 764.1 N.
So, the weight of the horse loaded onto the raft is 764.1 N.
mass of horse
= mass of water displaced (Archimedes principle)
= 0.027*4.2*6.5 m^3 * 1000 kg/m^3
= 737.1 kg
Weight of horse
= mg
= 737.1 * 9.81 N
= 7230 N