The density of a 6 foot tall man that weighs 840. Newtons fluctuates from a value slightly less than the density of water when the man completely inhales to a value slightly more than the density of water when the man completely exhales.
Note: Assume that the water pressure does not affect the volume of the man.
A)The man completely exhales and jumps into the deep end of a pool with a depth of 9 feet. The man sinks to the bottom of a pool and lands on a scale; at equilibrium, the scale reads 44.5 Newtons.
1)Calculate the buoyant force of the water acting on the man with his breath completely exhaled.
2)Calculate the volume of the man with his breath completely exhaled.
B)The man completely inhales and jumps into the deep end of a pool with a depth of 9 feet. The man swims to the bottom of a pool and stands erect on the bottom of the pool for a moment at rest. The man then accelerates upward due to an unbalanced vertical force (the buoyant force of the water acting on the man is greater than the weight of the man); the man moves upward 3 feet (0.914m) in 5.59 seconds when his head breaks the surface of the water.
1)Calculate the net acceleration of the man with his breath completely inhaled while totally submerged in the water.
2)Calculate the buoyant force of the water acting on the man with his breath completely inhaled.
3)Calculate the volume of the man with his breath completely inhaled.
C)Calculate the amount of air the man took in his breath for Part
A)
1) To calculate the buoyant force acting on the man, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Given that the scale reading is 44.5 Newtons, this is equal to the buoyant force.
2) To calculate the volume of the man with his breath completely exhaled, we can use the equation for density: density = mass/volume. Rearranging the equation to solve for volume, we get: volume = mass/density. The mass of the man is not given, so we need to calculate it using the weight provided and the acceleration due to gravity. Weight = mass x gravity, so rearranging the equation, we get: mass = weight/gravity. Once we have the mass, we can calculate the volume using the density of water.
B)
1) To calculate the net acceleration of the man with his breath completely inhaled, we need to use the equation of motion: acceleration = (final velocity - initial velocity)/time. In this case, the man is initially at rest, so the initial velocity is 0. The final velocity is the velocity when his head breaks the surface of the water, which is the distance traveled divided by the time taken to reach that point.
2) To calculate the buoyant force acting on the man with his breath completely inhaled, we can again use Archimedes' principle. The scale reading at equilibrium will give us the buoyant force.
3) To calculate the volume of the man with his breath completely inhaled, we can use the same equation density = mass/volume. The mass can be calculated using the weight and acceleration due to gravity, and then the volume can be calculated using the density of water.
C) The question does not provide enough information to directly calculate the amount of air the man took in his breath. Additional information, such as the change in volume or measurement of the inhaled breath, would be required.
A) The man completely exhales and jumps into the deep end of a pool with a depth of 9 feet. The man sinks to the bottom of the pool and lands on a scale; at equilibrium, the scale reads 44.5 Newtons.
1) Calculate the buoyant force of the water acting on the man with his breath completely exhaled.
The buoyant force is given by the equation:
Buoyant force = weight of the fluid displaced
Since the man sinks to the bottom of the pool and remains at equilibrium, the buoyant force must equal his weight.
Buoyant force = Weight of the man
Buoyant force = 44.5 Newtons
2) Calculate the volume of the man with his breath completely exhaled.
To calculate the volume of the man, we can use the equation:
Buoyant force = density of water * volume * acceleration due to gravity
Rearranging the equation, we get:
Volume = Buoyant force / (density of water * acceleration due to gravity)
We need to know the density of water and the acceleration due to gravity to calculate the volume.
B) The man completely inhales and jumps into the deep end of a pool with a depth of 9 feet. The man swims to the bottom of the pool and stands erect on the bottom of the pool for a moment at rest. The man then accelerates upward due to an unbalanced vertical force (the buoyant force of the water acting on the man is greater than the weight of the man); the man moves upward 3 feet (0.914m) in 5.59 seconds when his head breaks the surface of the water.
1) Calculate the net acceleration of the man with his breath completely inhaled while totally submerged in the water.
To calculate the net acceleration, we can use the equation:
Net force = mass * acceleration
Since the net force acting on the man is the difference between the buoyant force and the weight of the man, we can write the equation as:
Net force = (buoyant force - weight of the man)
Net acceleration = Net force / mass
We need to know the mass of the man to calculate the net acceleration.
2) Calculate the buoyant force of the water acting on the man with his breath completely inhaled.
The buoyant force is given by the equation:
Buoyant force = weight of the fluid displaced
Since the man is submerged in water and his breath is completely inhaled, the buoyant force will be equal to the weight of the water displaced by the volume of the man.
3) Calculate the volume of the man with his breath completely inhaled.
Similar to part A, we can use the equation:
Buoyant force = density of water * volume * acceleration due to gravity
To calculate the volume of the man, rearrange the equation as:
Volume = Buoyant force / (density of water * acceleration due to gravity)
We need to know the density of water and the acceleration due to gravity to calculate the volume.
C) To calculate the amount of air the man took in his breath for Part B, you will need to provide information such as the initial volume of his lungs before inhaling, the final volume of his lungs after inhaling, or any other relevant data.