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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:

E=mc^2

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.

Potential Energy and Momentum Question

A man with a mass of 65 kg skis down a friction-less hill that is 4.4m high. At the bottom of the hill the terrain levels out. As the man reaches the horizontal section, he grabs a 19-kgbackpack and skis off a 1.0 m-high ledge. At what horizontal distance from the edge of the ledge does the man land?

Combining Conservation Laws

A 15.0 kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00m/s horizontally to the left. Find the maximum distance tha

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

speed of the skier

A 40-kg skier pushes off the top of a hill with an initial speed of 4.0 m/s. Neglecting friction, how fast will she be moving after dropping 10 m in elevation? Please provide detailed explanation.

Eigenfunction and Momentum

I have attached a sheet with two problems. One on eigenfunctions and one on momentum for the ground state. 1. Show that the first two eigenfunctions for the particle in the box problem are orthogonal, i.e. that 2. Compute the average value of the momentum for the ground state (lowest energy) wave-function for a particle

Atomic and Nuclear Physics

An electron and a positron (an anti electron) make a head-on collision, each moving at v = 0.99999c. In the collision the electrons disappear and are replaced by two muons (each muon mc^2 = 105.7 MeV) that move off in opposite directions. What is the kinetic energy (MeV) of each of the muons?

Physics: Calculate the spring force constant k

See attachment. A 126 g ball is dropped from a height of 64.9 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.48716 cm. The acceleration of gravity is 9.8 m/s2. Calculate the spring force costant k. Answer in units of N/m

Energy conservation is examined.

Engineers at a national research laboratory built a prototype automobile that could be driven 180 miles on a single gallon of unleaded gasoline. They estimated that in mass production the car would cost $40,000 per unit to build. The engineers argued that Congress should force US Automakers to build this energy efficient car.

Mechanics: Spring and Mass System

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

Physics: Potential Energy and Energy Conservation

A 2.00 kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 37 degrees. a) What is the speed of the block as it slides along the horizontal sur

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.

Speed of Block When it Hits the Ground

The two blocks shown below are attached to a rope and wrapped around a pulley as shown. The pulley is a disk of mass 7.00 kg and radius 0.200 m The pulley and surface are frictionless and the system is release from rest. Use conservation of energy to find the speed of the object 2 when it hits the ground.

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

energy conservation in an eleastic system

A 60 kg trampoline artist jumps vertically upward from the top of a platform 3 meters high with a speed of 3.0 m/s. (a) How fast is he going as he lands on the trampoline, 3.0 m below? _______ m/s (b) If the trampoline behaves like a spring of spring constant 5.2 104 N/m, how far does he depress it? _______m

Physics - Potential Energy & Conservation

A 60 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 4.5 m/s. (a) How fast is he going as he lands on the trampoline, 3.0 m below? 1 ......m/s (b) If the trampoline behaves like a spring of spring constant 5.2 104 N/m, how far does he depress it? 2 .......m

Simple Harmonic Motion of pendulum

The length of a simple pendulum is 0.71 m, the pendulum bob has a mass of 311 grams, and it is released at an angle of 12° to the vertical. With what frequency (in hertz) does it vibrate? Assume simple harmonic motion. What is the pendulum bob's speed (in m/s) when it passes through the lowest point of the swing? What

Conservation of Momentum and Mechanical Energy

Please see the attachment. For the apparatus pictured below, one ball swinging in at a speed of 2vo will not cause two balls to swing out with speeds vo. (a) Which law of physics precludes this situation from happening, the law of conservation of momentum or the law of conservation of mechanical energy? (b) Prove this law ma

Simple mechanics

A toy car with mass 0.020 kg is propelled by a spring with constant 80 N/M onto a track. The track contains a loop of radius 0.10m. Ignore any losses due to friction and use g= 10m/s^2. What is the minimum compression of the spring neccessary for the car to complete the loop without leaving the track?

Fluids: Pressure of fluid column in a pipeline

Determine the water gauge pressure at a house at the bottom of a hill fed by a full tank of water 5.0 m deep and connected to the house by a pipe that is L = 65 m long at an angle of 60?from the horizontal (Fig. 10-47). Neglect turbulence, and frictional and viscous effects. N/m2 How high would the water shoot if it came vert

Gravitation: Potential energy, field, and force

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

Conservation of momentum: Example problem

If two objects collide and one is initially at rest, answer the following (ignore any frictional effects): a) Is it possible for both of them to be at rest after the collision? b) Is it possible for one of them to be at rest after the collision? c) Under what condition is their total energy conserved?

Draw two diagrams for the situation where a moving train collides with a train that is not moving, and the trains use their springy bumpers to bounce off each other without damage. One diagram should show the instant just before the collision and the other the instant just after the collision. Assume the trains do not have the same mass. Make sure you identify your isolated system. Solve for the final velocity of each train in terms of the initial velocity of the initially moving train.

Draw two diagrams for the situation where a moving train collides with a train that is not moving, and the trains use their springy bumpers to bounce off each other without damage. One diagram should show the instant just before the collision and the other the instant just after the collision. Assume the trains do not have the s