A thin spherical shell with mass of .4kg and diameter of .2m is filled with alcohol(density=806kg/m^3). It is then released from rest at the bottom of a pool of water,
Find the acceleration of the alcohol filled shell as it rises to the surface of the water.
asda
a=1.07m/s^2
To find the acceleration of the alcohol-filled shell as it rises to the surface of the water, we can use the principles of buoyancy and Newton's laws of motion.
First, let's calculate the volume and weight of the alcohol-filled shell:
1. Calculate the radius of the shell:
The diameter of the shell is given as 0.2 m, so the radius (r) is half of the diameter:
r = 0.2 m / 2 = 0.1 m
2. Calculate the volume of the shell:
The volume of a sphere can be calculated using the formula: V = (4/3) * π * r^3
V = (4/3) * 3.1416 * (0.1 m)^3
= 0.00418879 m^3
3. Calculate the mass of the alcohol:
The density of alcohol is given as 806 kg/m^3, and the volume of the shell is 0.00418879 m^3
So, the mass (m) of the alcohol is:
m = density * volume = 806 kg/m^3 * 0.00418879 m^3
= 3.375 kg (approximately)
4. Calculate the weight of the alcohol:
Weight (W) is given as mass multiplied by acceleration due to gravity (g):
W = m * g = 3.375 kg * 9.8 m/s^2
= 33.075 N (approximately)
Now, let's consider the forces acting on the alcohol-filled shell:
1. Buoyant force:
When the shell is submerged in water, it experiences an upward buoyant force equal to the weight of the water displaced by the shell.
2. Weight of the shell:
The shell also experiences the downward force due to its weight.
When the shell is released from rest, it is not moving initially. So the net force acting on it is the difference between the buoyant force and the weight of the shell:
Net Force = Upward Buoyant Force - Weight of Shell
Since the shell is released at the bottom of a pool of water, the buoyant force is greater than the weight of the shell. Therefore, the net force is positive and directed upward.
According to Newton's second law of motion, the net force is equal to the mass of the shell multiplied by its acceleration:
Net Force = m * a
So, we can equate the net force with the mass of the shell times its acceleration:
Upward Buoyant Force - Weight of Shell = m * a
Now, let's substitute the known values into the equation:
33.075 N - Weight of Shell = 3.375 kg * a
To find the acceleration, we need to solve for "a":
a = (33.075 N - Weight of Shell) / 3.375 kg
Substituting the weight of the shell (which is 33.075 N) into the equation:
a = (33.075 N - 33.075 N) / 3.375 kg
= 0 / 3.375 kg
= 0 m/s^2
Therefore, the acceleration of the alcohol-filled shell as it rises to the surface of the water is zero.