/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 61 Swimmer A swimmer moves through ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 61

Swimmer A swimmer moves through the water at a constant speed of \(0.22 \mathrm{~m} / \mathrm{s}\). The average drag force opposing this motion is \(110 \mathrm{~N}\). What average power is required of the swimmer?

Short Answer

Expert verified
24.2 W

Step by step solution

01

- Identify the given values

The swimmer's speed is given as \(v = 0.22 \; \text{m/s}\) and the average drag force opposing the swimmer is \(F = 110 \; \text{N} \).
02

- Write down the formula for power

The formula to calculate power is given by: \( P = F \times v \), where \(P\) is power, \(F\) is force, and \(v\) is velocity.
03

- Substitute the given values into the formula

Substitute the values into the formula to find the power: \( P = 110 \; \text{N} \times 0.22 \; \text{m/s} \).
04

- Calculate the power

Perform the multiplication: \( P = 110 \times 0.22 = 24.2 \; \text{W} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

average power
In physics, average power refers to the rate at which work is done over a specific period of time. It is calculated by the formula: power (P) is calculated as the product of the force applied (F) and the velocity (v). hence: In this case, the swimmer moves at a constant speed of 0.22 m/s and the drag force opposing the motion is 110 N. Hence, the required average power is calculated by the formula: P = F 脳 v P = 110 N 脳 0.22 m/s = 24.2 W. This means the swimmer exerts an average power of 24.2 watts to overcome the drag force while swimming.
drag force
Drag force is a type of resistance force that opposes the motion of an object through a fluid (like water or air). It is an important concept to understand when considering motion through fluids.
The drag force depends on several factors:
  • The shape of the object
  • The density of the fluid
  • The object鈥檚 speed
  • The surface area of the object facing the flow
In the context of the swimmer, the drag force is the resistance provided by the water as the swimmer moves through it. The average drag force opposing the swimmer鈥檚 motion is given as 110 N. This force must be countered by the swimmer's effort to maintain a constant speed.
velocity
Velocity is a vector quantity that includes both the speed and direction of an object's motion.
In this exercise, the swimmer moves at a constant speed of 0.22 m/s. Since the speed is constant, there is no acceleration, meaning the swimmer's velocity does not change over time.
Velocity is essential for calculating power, as power is influenced by how fast the swimmer is moving. The formula used to find power, P = F 脳 v, includes velocity as one of the key variables. So, the swimmer鈥檚 ability to maintain a steady velocity directly impacts the average power required.
constant speed
Nice work! You're making great strides in understanding constant speed. Constant speed means that the object is moving at a uniform pace over a period of time. There is no change in velocity. In this exercise, the swimmer moves at a constant speed of 0.22 m/s. A constant speed implies all the forces are in equilibrium. For the swimmer, this means the force exerted to move forward balances exactly with the opposing drag force (110 N). In other words, the swimmer's effort is steadily counteracting the water's resistance, keeping the velocity constant.
force and motion equations
Force and motion are fundamental concepts in physics. The relationship between force, mass, and acceleration is governed by Newton鈥檚 Second Law of Motion: \( F = ma \).
However, when dealing with constant speed and drag force, it鈥檚 more straightforward to consider the work-energy principle and power equations. In this exercise:
  • The swimmer exerts a force to overcome the drag force.
  • This force does work as the swimmer moves through the water.
  • The power needed is calculated using the formula: \( P = F \times v \).
The equilibrium of forces, where the swimmer's force matches the drag force, ensures constant speed. The average power (24.2 W) indicates the rate at which the swimmer鈥檚 work is done to counteract the drag force.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Freight Car A railroad freight car of mass \(3.18 \times 10^{4} \mathrm{~kg}\) collides with a stationary caboose car. They couple together, and \(27.0 \%\) of the initial kinetic energy is transferred to nonconservative forms of energy (thermal, sound, vibrational, and so on). Find the mass of the caboose. Hint: Translational momentum is conserved.

Cave Rescue A cave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. The lift is performed in three stages, each requiring a vertical distance of \(10.0 \mathrm{~m}:\) (a) the initially stationary spelunker is accelerated to a speed of \(5.00 \mathrm{~m} / \mathrm{s} ;\) (b) he is then lifted at the constant speed of \(5.00 \mathrm{~m} / \mathrm{s} ;\) (c) finally he is slowed to zero speed. How much work is done on the \(80.0 \mathrm{~kg}\) rescuee \(\quad F_{x}\) by the force lifting him during each stage?

Rebound to the Left A \(5.0 \mathrm{~kg}\) block travels to the right on a rough, horizontal surface and collides with a spring. The speed of the block just before the collision is \(3.0 \mathrm{~m} / \mathrm{s}\). The block continues to move to the right, compressing the spring to some maximum extent. The spring then forces the block to begin moving to the left. As the block rebounds to the left, it leaves the now uncompressed spring at \(2.2 \mathrm{~m} / \mathrm{s}\). If the coefficient of kinetic friction between the block and surface is \(0.30\), determine (a) the work done by friction while the block is in contact with the spring and (b) the maximum distance the spring is compressed.

Large Meteorite vs. TNT On August 10,1972, a large meteorite skipped across the atmosphere above western United States and Canada, much like a stone skipped across water. The accompanying fireball was so bright that it could be seen in the daytime sky (see Fig. \(9-22\) for a similar event). The meteorite's mass was about \(4 \times 10^{6} \mathrm{~kg}\) : its speed was about \(15 \mathrm{~km} / \mathrm{s}\). Had it entered the atmosphere vertically, it would have hit Earth's surface with about the same speed. (a) Calculate the meteorite's loss of kinetic energy (in joules) that would have been associated with the vertical impact. (b) Express the energy as a multiple of the explosive energy of 1 megaton of \(\mathrm{TNT}\), which is \(4.2 \times 10^{15} \mathrm{~J}\). (c) The energy associated with the atomic bomb explosion over Hiroshima was equivalent to 13 kilotons of TNT. To how many Hiroshima bombs would the meteorite impact have been equivalent?

Given \(x(t)\) A force acts on a \(3.0 \mathrm{~kg}\) particle-like object in such a way that the position of the object as a function of time is given by \(x=(3 \mathrm{~m} / \mathrm{s}) t-\left(4 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}+\left(1 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}\) with \(x\) in meters and \(t\) in seconds Find the work done on the object by the force from \(t_{1}=0.0 \mathrm{~s}\) to \(t_{2}=4.0 \mathrm{~s}\). (Hint: What are the speeds at those times?)
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Thermodynamics

Read Explanation

Energy Physics

Read Explanation

Particle Model of Matter

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Rotational Dynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.