A large air-filled rubber ball is tethered to the bottom of a swimming pool. The tension in the tether is 100N. The mass of the rubber in the ball itself is 2kg while pwater=1000kgm(-3) and pair=1.2 kgm(-3). What is the volume of the ball?
tension-weight=bouyancy
tension-2*g - pair*volume=pwater*volume
solve this for volume.
Well, water, water, everywhere! Let's dive into this question.
First, let's figure out the buoyant force acting on the ball. The buoyant force is equal to the weight of the water displaced by the ball. Since the ball is submerged in a swimming pool, the buoyant force is equal to the weight of the water column above the ball.
Now, the ball is tethered to the bottom of the pool, so we need to find the tension in the tether. The tension in the tether is equal to the weight of the ball plus the buoyant force acting on it.
The weight of the ball is simply the mass of the ball multiplied by the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the mass of the ball is given as 2 kg, so the weight of the ball is 2 kg * 9.8 m/s^2 = 19.6 N.
Since the tension in the tether is given as 100 N, we can subtract the weight of the ball from the tension to find the buoyant force: 100 N - 19.6 N = 80.4 N.
Now, let's use the definition of buoyant force to find the volume of the ball. The buoyant force is equal to the weight of the water displaced by the ball, which is equal to the weight of the water with a volume equal to the volume of the ball.
Using the formula for weight, which is equal to mass multiplied by the acceleration due to gravity, we can find the weight of the water displaced by the ball.
The volume of the ball can be calculated using the formula:
Volume = weight of water / (density of water - density of air)
Using the given values, the density of water (pwater) is 1000 kg/m^3, and the density of air (pair) is 1.2 kg/m^3.
Now, let's put it all together and calculate the volume of the ball!
Volume = 80.4 N / (1000 kg/m^3 - 1.2 kg/m^3) = 80.4 N / 998.8 kg/m^3 = 0.0805 m^3.
So, the volume of the ball is approximately 0.0805 cubic meters. That's enough space to make quite the splash!
To find the volume of the ball, we can use the principle of buoyancy.
The buoyant force acting on the ball is equal to the weight of the water displaced by the ball. The buoyant force is given by the equation:
Buoyant force = Weight of water displaced
The weight of water displaced is equal to the weight of the ball in air minus the tension in the tether. We can calculate the weight of the ball in air using its mass and the acceleration due to gravity:
Weight of ball in air = mass of ball * acceleration due to gravity
Weight of ball in air = 2 kg * 9.8 m/s^2
Weight of ball in air = 19.6 N
Now we can calculate the weight of water displaced:
Weight of water displaced = Weight of ball in air - Tension in tether
Weight of water displaced = 19.6 N - 100 N
Weight of water displaced = -80.4 N (Note that the negative sign indicates that the buoyant force is in the upward direction)
Using the equation for the weight of water displaced:
Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity
Plugging in the known values:
-80.4 N = 1000 kg/m^3 * volume of water displaced * 9.8 m/s^2
Rearranging the equation to solve for the volume of water displaced:
Volume of water displaced = -80.4 N / (1000 kg/m^3 * 9.8 m/s^2)
Volume of water displaced = -0.00826 m^3
Since volume cannot be negative, we can ignore the negative sign. Therefore, the volume of the ball is 0.00826 m^3.
To find the volume of the ball, we can use the concept of buoyancy. Buoyancy is the upward force exerted on an object submerged in a fluid. In this case, the ball is submerged in water.
The buoyant force can be calculated using the formula:
Buoyant force = weight of the fluid displaced
In this scenario, the buoyant force acting on the ball is equal to the tension in the tether, which is 100N.
First, we need to find the weight of the fluid displaced by the ball. We can calculate this as the difference between the weight of the ball in air and the weight of the ball in water.
Weight of the ball in air = mass of the ball * acceleration due to gravity
= 2kg * 9.8m/s^2
= 19.6N
Weight of the ball in water = weight of the ball in air - buoyant force
= 19.6N - 100N
= -80.4N
Since the ball is negatively buoyant, its weight in water is greater than the buoyant force. This indicates that the volume of the ball must be greater than the volume of water displaced.
To find the volume of water displaced (Vwater), we can use the formula:
Vwater = (Weight of the ball in air - Weight of the ball in water) / density of water.
Substituting the values:
Vwater = (-80.4N) / (1000kg/m^3)
= -0.0804m^3
Since volume cannot be negative, we take the absolute value:
Vwater = 0.0804m^3
Therefore, the volume of the ball is approximately 0.0804m^3.