Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q40 PE

Expert-verified
College Physics (Urone)
Found in: Page 262
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

(a) What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months?

(b) How long can a battery that can supply 8.00×104 J run a pocket calculator that consumes energy at the rate of 1.00×10−3 W?

(a) The energy content of available for the battery is \(93.31 \times {10^6}{\rm{ J}}\).

(b) The battery can be used up to \(2.54{\rm{ years}}\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Definition of Concepts

Power: Power is a scalar quantity which is defined how fast the energy is being used.

Mathematically,

\(P = \frac{E}{T}\) (1.1)

Here, E stands for energy, and T stands for time.

Find the energy content of the battery

(a)

The expression for the energy content of the battery can be calculated using equation (1.1).

Rearranging equation (1.1) in order to get an expression for the energy content.

\(E = PT\)

Here, P is the power of battery \(\left( {P = 2.00{\rm{ W}}} \right)\) and T is the time \(\left( {T = 18{\rm{ months}}} \right)\).

Putting all known values,

\(\begin{aligned}E &= \left( {2.00{\rm{ W}}} \right) \times \left( {18{\rm{ month}}} \right)\\ &= \left( {2.00{\rm{ W}}} \right) \times \left( {18{\rm{ month}}} \right) \times \left( {\frac{{30{\rm{ day}}}}{{1{\rm{ month}}}}} \right) \times \left( {\frac{{24{\rm{ hr}}}}{{1{\rm{ day}}}}} \right) \times \left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ h}}}}} \right)\\ &= 93.31 \times {10^6}{\rm{ J}}\end{aligned}\)

Therefore, the energy content of available for the battery is \(93.31 \times {10^6}{\rm{ J}}\).

Find the life of the battery

(b)

The life of the battery is,

\(T = \frac{E}{P}\)

Here, E is the energy contain of the battery \(\left( {8.00 \times {{10}^4}{\rm{ J}}} \right)\), and P is the power \(\left( {1.00 \times {{10}^{ - 3}}{\rm{ W}}} \right)\).

Putting all known values,

\(\begin{aligned}T &= \frac{{8.00 \times {{10}^4}{\rm{ J}}}}{{1.00 \times {{10}^{ - 3}}{\rm{ W}}}}\\ &= \left( {8.00 \times {{10}^7}{\rm{ sec}}} \right) \times \left( {\frac{{1{\rm{ hr}}}}{{3600{\rm{ s}}}}} \right) \times \left( {\frac{{1{\rm{ day}}}}{{24{\rm{ hr}}}}} \right) \times \left( {\frac{{1{\rm{ year}}}}{{365\,{\rm{day}}}}} \right)\\ &= 2.54{\rm{ years}}\end{aligned}\)

Therefore, the battery can be used up to \(2.54{\rm{ years}}\).

Most popular questions for Physics Textbooks

Calculate the power output in watts and horsepower of a shot-putter who takes \(1.20{\rm{ s}}\) to accelerate the \(7.27 - {\rm{kg}}\) shot from rest to \(14.0{\rm{ m}}/{\rm{s}}\), while raising it \(0.800{\rm{ m}}\). (Do not include the power produced to accelerate his body.)

(a) Find the useful power output of an elevator motor that lifts a \(2500 - {\rm{kg}}\) load a height of \(35.0{\rm{ m}}\) in \(12.0{\rm{ s}}\), if it also increases the speed from rest to \(4.00{\rm{ m}}/{\rm{s}}\). Note that the total mass of the counterbalanced system is \(10,000{\rm{ kg}} - \)so that only \(2500{\rm{ kg}}\) is raised in height, but the full \(10,000{\rm{ kg}}\) is accelerated.

(b) What does it cost, if electricity is \(\$ 0.0900{\rm{ per kW}} \cdot {\rm{h}}\)?

The swimmer shown in Figure 7.44 exerts an average horizontal backward force of 80.0 N with his arm during each 1.80 m long stroke.

(a) What is his work output in each stroke?

(b) Calculate the power output of his arms if he does 120 strokes per minute.

Figure 7.44

Consider humans generating electricity by pedaling a device similar to a stationary bicycle. Construct a problem in which you determine the number of people it would take to replace a large electrical generation facility. Among the things to consider are the power output that is reasonable using the legs, rest time, and the need for electricity 24 hours per day. Discuss the practical implications of your results.

Confirm the value given for the kinetic energy of an aircraft carrier in Table 7.1. You will need to look up the definition of a nautical mile (1 knot = 1 nautical mile/h).
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Physics of Motion

Read explanation

Scientific Method Physics

Read explanation

Fluids

Read explanation

Torque and Rotational Motion

Read explanation

Nuclear Physics

Read explanation

Fields in Physics

Read explanation

Measurements

Read explanation

Space Physics

Read explanation

Electricity

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Electrostatics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Mechanics and Materials

Read explanation

Engineering Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Particle Model of Matter

Read explanation

Waves Physics

Read explanation

Magnetism

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Linear Momentum

Read explanation

Rotational Dynamics

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Geometrical and Physical Optics

Read explanation

Thermodynamics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Electric Charge Field and Potential

Read explanation

Turning Points in Physics

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.