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Conservation of Energy

The law of conservation of energy states that the total amount of energy in an isolated system remains constant over time. In an isolated system, this law states that energy is localized and can change its location within the system, it can change form within the system. However, two initially isolated systems with no external interactions can be composed into a single isolated system. The total amount of energy of the composite system is equal to the sum of the respective total amounts of energy of the two component systems.

The conservation of mass, previously called vis viva, or living force was first attempted to be explained in 1676-1689 by Gottfried Wilhelm Leibniz. The equation was changed multiple times until 1807 when Thomas Young recalibrated it to:

1/2 ∑_i =〖m_i v_i^2 〗

The conservation of energy has played a major role in the development thermodynamics, specifically the first law of thermodynamics. The first law of thermodynamics is:

δQ=dU+ δW

Where δQ is the amount of energy added to the system by a heating process, δW is the amount of energy lost by the system due to work done by the system on its surroundings and dU is the change in the internal energy of the system.

Conservation of energy over time in special relativity was described by Albert Einstein. It states the relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion. The equation is:


Ecology, Ecosystems

3. What is the role of natural cycles and what part do we play in your ecosystem? Discuss three natural cycles and their effects. What do species do to adapt? Be specific. 4. Name four ways quality of life and sustainability can be enhanced. Name four (4) ways you can create a structure for these sustainability qualities. Be

Pion photo production

Consider the process γ + p → p + π0 ( π0 photoproduction) with the proton at rest. Find the minimum energy of the photon Eγ.

Developing an Energy Plan

Your organization is about to review their energy use and develop an energy plan, including as many renewable power sources as possible. Please explain the following: 1. The law of conservation of energy with an explanation of how this law applies to energy use and energy conversions. 2. The pros and cons of the foll

Spring system with mass attached and dropped

A spring (k = 400 N/m) is hung vertically. a) If a 5 kg mass is attached to the end of the spring and gently lowered to rest position, what will be the stretch of the spring? b) If the 5 kg mass is attached and simply dropped, what will be the maximum velocity and the maximum stretch? I know the anwer to the first part.

Center of Mass Theorem: Velocity of bullet, compression of the spring

Please see attached file for a diagram. Two identical wood blocks, A and B, both of mass M, are fastened to the ends of a spring. The spring constant is k. Both blocks are placed on a frictionless horizontal table. Initially, both blocks are at rest and the spring has its unstretched length. A bullet of mass m (m<<M) is

Impulse Momentum, Conservation of Linear Momentum, collisions,

See attached file. The problems came out from Physics 7th edition by Cutnell and Johnson, chapter 7. The sections include 1) the impulse-- momentum theorem 2) the principle of conservation of linear momentum 3) collisions in one dimension 4) collisions in two dimensions and 5) center of mass.

Oscillation, Motion and Energy

A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 461 Hz and a maximum displacement of 0.57 mm. What are the (a) angular frequency, (b) maximum speed, and (c) magnitude of the maximum acceleration? A 7.66 kg object on a horizontal frictionless surface is attached to a spring with k = 2

Mass attached to a spring is released: Frequency and amplitude of SHM

82. A massless spring with spring constant 19 N/m hangs vertically. A body of mass 0.20 kg is attached to its free end and then released. Assume that the spring was unstretched before the body was released. Find (a) how far below the initial position the body descends, and the (b) frequency and (c) amplitude of the res

Gravitation: Potential energy, field, and force and circular motion.

A. Height of a Projectile A projectile is fired straight up from the south pole of earth with an initial speed of 8.0km/s. Find the maximum height it reaches, neglecting effects due to air resistance. b. Speed of a Projectile. A projectile is fired straight up from the south pole of earth with an initial speed of 15.0k

Two particles collide. To determine speeds, angles etc after collision.

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90 degree;. a) at what angle does the target particle move after the collision? b) what are the final speeds of the two particles? c) what fraction of the initial kinetic energy is tr

Potential energy and conservation of energy and linear momentum

1.) The two masses in the Atwood's machine shown in the figure below are initially at rest at the same height. After they are released, the large mass, m2, falls through a height h and hits the floor, and the small mass, m1, rises through a height h. a.) Find the speed of the masses just before m2 lands. Assume the ropes and

2D motion of a projectile

A block of mass m slides down a frictionless incline. The block is released at height h above the bottom of the loop (see file for drawing of path). a. What is the force on the inclined track on the block at point A b. What is the force on the inclined track at point B c. At what speed does the block leave the track at poin

Fresnel's equations

A linearly polarized electromagnetic wave is incident on the plane interface between air and an isotropic medium of relative permittivity &#949; = 3 and relative permeability &#956; = 1. The incident propagation vector makes an angle of 60o with the normal to the interface and the direction of polarization of the incident wave i

Calculations for Work, Potential Energy, and Power

An iron ball having a mass of 5 kg is lifted from the floor to a height of 2.5 meters above the floor. a) How much work was done to lift the ball? b) How much potential energy did the ball gain? c) If the motor lifting the ball raises it 2.5 meters in ten seconds, what is its power? If a 600 kg car is moving with a s

rotation, rotational kinetic energy, spring

Please see attachment. Thank You your help is greatly needed! 24. A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision? 25. A 50-kg rider on a moped of mass 75

Calculations with a Ballistic Pendulum

In a ballistic pendulum an object of mass m is fired with an initial speed v_0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement theta as shown a). Find an expression for

Electric Potential Difference Created by Point Charges

I have a test coming up and I can't seem to grasp the concept of this particular part of the chapter. Here are two sample problems that I am having the most difficulty with. 1.) One particle has a mass of 3.00 10-3 kg and a charge of +7.60 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two parti

Simple harmonic motion

Please see attached file for detailed description. 34. Block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 7.0 rad/s. The drawing indicates the position of the block when the spring is unstrained. T

Momentum and Angular Momentum

Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that is begins to slide down, through what vertical hight will it descend before it leaves the surface of the sphere?[Hint: Use conservation of energy to find the puck's speed as a function of its height, the

Work, Energy, and Momentum

1. An iron ball having a mass of 5 kg is lifted from the floor to a height of 2.5 meters above the floor. a) How much work was done to lift the ball? b) How much potential energy did the ball gain? 2. If a 600 kg car is moving with a speed of 25 m/s, that what is its kinetic energy? Put your answer in Joules.

Kinetic Friction of Object on Horizontal Spring

Object on a spring is horizontally compressed 5.00m from its equilibrium position, is released and stops at 19.8m away. Spring's constant is 95 N/m. Assuming the object's mass is 60kg: A) What is the coefficient of kinetic friction between the object and the floor? B) What was the object's velocity and acceleration?

The Lagrangian Formulation of Mechanics

A ring of mass m slides on a smooth vertical rod. Attached to the ring is a light, inextensible string passing over a smooth peg located distance a from the rod. At the other end of the string is a mass M (M > m). The ring is released from rest at the same level as the peg. Determine, in terms of M,a, and m, the maximum distance