Question

If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter.

Short answer

A belly flop spreads out the person's energy (and momentum) over the surface of the water causing more particles of water to absorb energy (and momentum). Therefore, the person does not have as much energy (and momentum) to move more deeply into the water than if a "dive" is used to enter the water.

Step-by-step solution

Conservation of Energy

When a swimmer dives into water, he reaches to the deepest of the water than what he does in a belly flop and this phenomenon can be explained in terms of conservation of energy.

According to the conservation of energy, the total energy of the isolated system remains constant and also for an isolated system

${\mathit{F}}_{\mathbf{n}\mathbf{e}\mathbf{t}}\mathbf{=}\mathbf{0}\mathit{N}$

Newton’s Law

Newton’s second law of motion states that the net external force is the ratio between the change in momentum and change in time. Mathematically,

$F_{net}=\frac{\Delta p}{\Delta t}$

Where$∆p$ is the change in momentum,$∆t$is the change in time and$F_{net}$is the total external force.

Now the diver has a change in momentum as$∆p_1$ and water splashed is$∆p_2$and according to the law of conservation of mass we know that

$\Delta p_1+\Delta p_2=constant$

Momentum

Now if the diver does the belly flop the splashed water is more than the water splashed during the dive.

Momentum depends on mass and energy. Since the water splashed during the belly flop is much more, $∆p_2$is much more in case of belly flop which results in the decrease of$∆p_1$

Conclusion

The mass of the diver is unchanged. Since the energy is conserved,$∆p_1$ for the dive will be more. Hence the swimmer will get more velocity in case of dive and this will result in the increase in depth of the water.