Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the dive, the diver is 10.8 m above the surface of the water. Does the diver do work on entering the water? Explain.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

First, understand the concept of work in physics. Work is done when a force causes displacement. The formula for work is \( W = F \times d \times \cos(\theta) \), where \( F \) is the force applied, \( d \) is the displacement, and \( \theta \) is the angle between the force and the direction of displacement.

Next, consider the diver's situation. As the diver enters the water, the force exerted by the diver is due to gravity, which acts downward. The displacement is also downward, into the water.

Calculate the force exerted by the diver due to gravity. This force is the diver's weight, which can be calculated using \( F = m \times g \), where \( m \) is the mass of the diver (52.0 kg) and \( g \) is the acceleration due to gravity (approximately 9.8 m/s²).

Determine the displacement of the diver as they enter the water. The displacement is the distance from the apex of the dive to the surface of the water, which is 10.8 m.

Finally, analyze whether work is done. Since the force and displacement are in the same direction (both downward), \( \cos(\theta) = 1 \). Therefore, work is done by the diver on the water as they enter it, calculated using the formula \( W = F \times d \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Work in Physics

In physics, work is defined as the transfer of energy that occurs when a force is applied over a distance. It is calculated using the formula W = F × d × cos(θ), where W is work, F is the force applied, d is the distance moved in the direction of the force, and θ is the angle between the force and the direction of motion. In the context of the diver, understanding whether the diver exerts a force while entering the water is crucial to determining if work is done.

Kinetic and Potential Energy

Kinetic energy is the energy of an object due to its motion, while potential energy is the energy stored in an object due to its position in a gravitational field. As the diver falls, potential energy is converted into kinetic energy. At the moment of entering the water, the diver's kinetic energy is at its maximum, and understanding this energy transformation is essential for analyzing the work done during the entry.

Force of Water Resistance

When the diver enters the water, the water exerts an upward force known as water resistance or drag. This force opposes the motion of the diver and plays a significant role in the dynamics of the entry. To determine if the diver does work upon entering the water, one must consider the interaction between the diver's motion and the resistance force exerted by the water, which affects the overall energy transfer.

Related Practice

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Textbook Question

Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the dive, the diver is 10.8 m above the surface of the water. (b) Assuming that all the potential energy of the diver is converted into kinetic energy at the surface of the water, at what speed, in m/s, will the diver enter the water?

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At 25 °C (approximately room temperature) the rms velocity of an Ar atom in air is 1553 km/h. (c) What is the total kinetic energy of 1 mol of Ar atoms moving at this speed?

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Consider the following acid-neutralization reactions involvingthe strong base NaOH(aq):HNO31aq2 + NaOH1aq2¡NaNO31aq2 + H2O1l2HCl1aq2 + NaOH1aq2¡NaCl1aq2 + H2O1l2NH4+1aq2 + NaOH1aq2¡NH31aq2 + Na+1aq2 + H2O1l2(d) In the third equation NH4+1aq2 is acting as an acid. Basedon the value of H° for this reaction, do you think it is astrong or a weak acid? Explain.

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