A 80 kg diver steps off a 10 m tower and drops from rest straight down into the water. If he comes to rest 5.0 m beneath the surface, determine the average resistance force exerted on him by the water.
mg(10+5)=avgForce*5
Potential energy lost= workdone to water
2352
To determine the average resistance force exerted on the diver by the water, we need to use the concept of work done and the principle of conservation of energy.
The work done on an object is given by the formula:
Work = Force × Distance × cos(θ)
In this case, the force is the average resistance force exerted by the water on the diver, the distance is the depth the diver sinks into the water (5.0 m), and the angle (θ) is 0 degrees because the force and displacement are in the same direction.
The work done on the diver is also equal to the change in potential energy. The potential energy can be calculated using the formula:
Potential Energy = Mass × g × Height
where Mass is the mass of the diver (80 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and Height is the height from which the diver falls (10 m).
Setting the work done equal to the change in potential energy, we have:
Force × Distance × cos(0°) = Mass × g × Height
Rearranging the equation and solving for Force:
Force = (Mass × g × Height) / Distance
Substituting the given values:
Force = (80 kg × 9.8 m/s^2 × 10 m) / 5.0 m
Calculating the expression:
Force = 1568 N
Therefore, the average resistance force exerted on the diver by the water is 1568 Newtons.