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# Energy

Energy is an indirectly observed quantity which comes in many forms. There are many forms of energy such as, kinetic energy, potential energy, radiant energy and many more. Energy is an indispensable prerequisite for performing mechanical work and the concept has great important in natural science.

Energy as a concept emerged out of the idea of living force, which was defined as the product if the mass of an object and its velocity squared. It is believed that the living force is conserved.

The law of conservation of energy was first postulated in the 19th century. It was applied to isolated systems. Noether’s theorem states the conservation of energy is a consequence of the fact that the laws of physics do not change over time.

Energy can be used in different contexts in which energy is used. In chemistry, energy is used to describe heat being released from chemical reactions. In biology, energy is responsible for growth and development of organisms. In earth sciences, energy describes the movement of tectonic plates. Humans input energy to sustain life through calories via food.

Energy density is a term used to denote the amount of useful energy stored in a given system or region of space per unit volume. For example, nuclear reactions have a much higher energy density than coal combustion reactions.

### Newtons Law, Rotational Motion and Simple Harmonic Motion

A horizontal force of 50 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m O.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant: (a) Calculate the total energy expended

### Harmonic vibration of a mass

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration, calculate: (a) (i) the frequency of vibration. (ii) the maximum velocity of the mass during the vibration. (iii) the maximum acceleration of the

### Conservation of Energy and Projectile

There is a new ride at the amusement park this summer designed specifically for overachieving physics students! For this ride you allow a compressed spring to launch you towards a tank filled with hungry sharks. You first slide down a 40 degree slope then up a 30 degree slope which launches you over the shark tank. However, t

### Understanding Oscillatory Motion

Describe, in detail, oscillatory motion with specific reference to simple harmonic motion.

### Potential Energy Function and Force

Please see the attached file. a) Write down, in the form F(x) i, the force that gives rise to this potential function. b) The total energy of the system is a constant, E. For each of the following values of E state, with a reason, a range of ranges (accurate to one decimal place) of x-values that could represent a motion o

### System of springs: Energy stored in different springs

You can assume that air resistance and other frictional forces can be ignored in this question See attachment a) Define a datum for the gravitational potential energy of particle P. b) Write down the gravitational potential energy of particle P at a general point of motion. c) Write down the kinetic energy of a particl

### Understanding Pseudo Force

What is a pseudo force? Explain with the help of an appropriate example. Solve the following problem using the concept of pseudo force: Two rectangular blocks are stacked one over the other on a table. The lower and upper blocks have masses of 25 kg and 5 kg respectively. The coefficient of kinetic friction between the

### A half harmonic oscillator

Consider the corresponding problem for a particle confined to the right-hand half of a harmonic-oscillator potential: V(x) = infinity, x< 0 V(x) = (1/2)Cx^2, x >= 0 a. Compute the allowed wave function for stationary states of this system with those for a normal harmonic oscillator having the

### Prolate nuclear core and rotational bands

1. Consider a deformed prolate nuclear core consisting of an even number of neutrons and one even number of protons outside of this core is a neutron in a d5/2 state a. What would the degeneracy of the state be if the deformation were zero? b. What would be in the single particle shell model for deformed nuclei

### Internal enrgy and entropy of a Van der waals gas

7.4 Consider n moles of a Van der Waals gas. Show that (dU/dV)_T = n^2a/V^2. Hence show that the internal energy is U = the integral from zero to T of C_vdT - an^2/V + U0 where U0 is a constant. {Hint: Express U = U(T,V)}. 7.5 As in the previous question, consider n moles of Van der Waals gas. Show that (a) S = the in

### hydrogen with a nucleus of finite mass

The spectrum of hydrogen with a nucleus of ﬁnite mass. The analysis in Section I-7 of the text assumes that the nucleus remains ﬁxed as the electron orbits about it. This corresponds to assuming that the proton mass is effectively inﬁnite. More correctly. we should picture the proton and electron as orbiting about their co

### Finding the Potential Energy and Magnitude of Force

1. If a certain spring stretches 8.93072 cm when a load of 18.6372 N is suspended from it, how much will the spring stretch if it is cut in half and when 30.2799 N is suspended from it? Answer in units of cm 2.A certain spring stretches 4.5 cm when it supports a mass of 0.77 kg. If the elastic limit is not reached, how far w

### A proton in a well

The figure [attached] shows electric potential V along an x axis. A proton is to be released at x = 3.5 cm with initial kinetic energy 3.5 eV. The scale of the vertical axis is set by Vs = 10.0 V. (a) If it is initially moving in the negative direction, it either reaches a turning point (if so, what is the x coordinate of th

### Transition Energies in Ionized Lithium

A photon with energy in the visible region (between about 4000 and 7000 A) causes the transition n --> n + 1 in doubly ionized lithium, Li++, a hydrogen-like system with a single electron and a central charge equal to 3e. What is the lowest value of n for which this could occur?

A radio station broadcasts at a frequency of 1MHz with a total radiated power of 5000 watts. (a) What is the wavelength of this radiation? (b) What is the energy (in electron-volts) of the individual quanta that compose the radiation? How many photons are emitted per second? per cycle of oscillation? (c) A certain radio rec

### Frequency and Energy of Photons

Consider an x-ray machine with a step-up transformer consisting of a primary coil of 100 turns and a secondary one with 50000 turns. If the voltage applied across the primary coil is 100 volts, and the minimum wavelength of a bremsstrahlung photon emitted by the x-ray tube, what is the frequency and energy of the photon?

### Smallest Value for E

An atomic particle is confined inside a rectangular box of sides a, b, c. The particle is described by a wave function that satisfies the Schrodinger wave equation [see the attachment] The wave function is required to vanish at each surface of the box (but not identically zero). This condition imposes constraints on the se

### Activity for simulating the periodic table

Imagine that you want to create an activity for a group of children to simulate the periodic table. Suggest items that you may use and how they may be organized in rows and columns. If you have some ideas I'd like to learn from you and also if you know books or internet sites let me know so I can read and understand more.

### Maximum Speed of Mass, Potential Energy & Spring Constant

The position of a 0.500 kg spring as a function of time is given as x(t) = (1.25 m)cos(6.00 t). What is the maximum speed of the mass? (7.5 m/s) What is the spring constant for this spring? (18 N/m) What is the maximum potential energy of this spring? (14 J) The answers given are in parenthesis. I'm just stuck.

### Taking Advantage of Alternative Energy Sources

Why is it that our society has not taken advantage of alternative energy sources?

### Machlett Dynamax X-Ray Tube

Please provide assistance for the following problems. step by step calculations are given. Question: 1. Consider an Machlett Dynamax x-ray tube with a tungsten target operating with an accelerating potential of 100 kV and filament current of 4.4A. The anode target angle is 17 degrees and the apparent focal spot is 1 mm by 1

### Probable and Physical Energy

I need help with the following physics exercise attached. ** Please see the attached file for the complete problem description ** A) Calculate the most probable energy B) Calculate the average energy

### Kinetic Energy and inertial coordinate systems

3.) Show that the kinetic energy of a multi-body system can be written in terms of the kinetic energy of the center of mass plus the kinetic energy relative to the center of mass. Start with the definition of the kinetic energy relative to an inertial coordinate system.

### The angular speed of a wheel increases at a constant rate of 1.5 rad/s^2

Please see attachments for details. 11. The angular speed of a wheel increases at a constant rate of 1.5 rad/s2. During a certain 3.2 s time interval, it makes four complete revolutions. If the wheel started from rest, how long has it been in motion at the start of this time interval? 12. An airplane makes a circular turn

### Gravitational Forces among the Four Objects

1.Three solid spheres of lead, each of mass 9.8 kg, are located at three corners of a square with side lengths of 50 cm. A small object is released at the forth corner. Considering only the gravitational forces among the four objects, determine the magnitude and direction of the acceleration of the smaller object when it is rele

### Friction and Temperature Change Problem

A crate of fruit with a mass of 35.0 kg and a specific heat capacity of 3800 J/kg.K slides 8.30m down a ramp inclined at an angle of 40.0 degrees below the horizontal (acceleration due to gravity is 9.81m/s^2). If the crate was at rest at the top of the incline and has a speed of 2.40m/s at the bottom, the work (W_f) done

### Electrical Energy Question

A dam covers an area 2000m long and 1500m wide, with a depth of 40 metres. If the centre of the dam sits 300m above a turbine through which all of the water will be passed, what is the total electrical energy (in TJ) that can be derived if the dam is completely emptied? (Assume no losses. g=9.81 m.s-2 and the density of water is

### Power Consumption and Production

In the year 2011, the United States used about 115EJ of energy. 1. How many large power plants need to operate to meet that need? A large power plant provides about 1000MW. 2. If each square mile of a wind farm provides 3MW, how many square miles of wind farms would the US need? 3. How does this compare (use ratios) to

### Solving nuclear physics problems

a. What is the highest energy to which alpha particles can be accelerated in a dc accelerator with 3 MV maximum voltage? b. Calculate the energy of a 1 MeV gamma-ray photon after Compton scattering through 90 degrees. Please show me a stepwise solution for how to reach the final answer.

### Sound Intensity and loudness

The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 Ã- 10-10 W/m2. What is the intensity level in dB?