Answer: the work done by the force is 0
Explanation:
F (x², xy)
121 = 11²
so R = x² + y² = 11²
p = x². Q = xy
Δp/Δy = 0, ΔQ/Δx
using Green's theorem
woek = c_∫F.Δr = R_∫∫ ΔQ/Δx - Δp/Δy) ΔA
= (x² + y² = 121)_∫∫ yΔA
now let x = rcosФ, y = rsinФ
ΔA = rΔrΔФ
so r from 0 to 11
and Ф from 0 to 2π
= 0_∫^2π 0_∫^11 rsinФ × rΔrΔФ
= 0_∫^2π SinФΔФ 0_∫^11 r²Δr
= [ -cosФ]^2π_0 [r³/3]₀¹¹ = ( -cos2π + cos0) (11³/3) = 0
therefore the work done by the force is 0
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. This law means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
It may be produced by
<span>Most of us use the word ‘heat’ to mean something that feels warm, but science defines heat as the flow of energy from a warm object to a cooler object.</span><span>Actually, heat energy is all around us – in volcanoes, in icebergs and in your body. All matter contains heat energy.</span><span>Heat energy is the result of the movement of tiny particles calledatoms, molecules or ions in solids, liquids and gases. Heat energy can be transferred from one object to another, and the transfer or flow due to the difference intemperature between the two objects is called heat.</span><span>For example, an ice cube has heat energy and so does a glass of lemonade. If you put the ice in the lemonade, the lemonade (which is warmer) will transfer some of its heat energy to the ice. In other words, it will heat up the ice. Eventually, the ice will melt and the lemonade and water from the ice will be the same temperature. This is known as reaching a state of thermal equilibrium.</span>Moving particles<span>Matter is all around you. It is everything in the universe – anything that has both mass andvolume and takes up space is matter. Matter exists in different physical forms – solids, liquids and gases.</span>All matter is made of tiny particles called atoms, molecules and ions. These tiny particles are always in motion – either bumping into each other or vibrating back and forth. It is the motion of particles that creates a form of energy called heat (or thermal) energy that is present in all matter.<span>Image: Particles in collision</span>The particles in solids are tightly packed and can only vibrate. The particles in liquids also vibrate but are able to move around by rolling over each other and sliding around. In gases, the particles move freely with rapid, random motion.Transferring heat energy – particles in collision<span>At higher temperatures, particles have more energy. Some of this energy can be transmitted to other particles that are at a lower temperature. For example, in the gas state, when a fast moving particle collides with a slower moving particle, it transfers some of its energy to the slower moving particle, increasing the speed of that particle.</span><span>With billions of moving particles colliding into each other, an area of high energy will slowly transfer across the material until thermal equilibrium is reached (the temperature is the same across the material).</span>Changing states by heat transferFaster moving particles ‘excite’ nearby particles. If heated sufficiently, the movement of particles in a solid increases and overcomes the bonds that hold the particles together. The substance changes its state from a solid to a liquid. If the movement of the particles increases further in the liquid, then a stage is reached where the substance changes into a gas.Three ways of transferring heat energy<span><span>All heat energy, including heat generated by fire, is transferred in different ways:<span><span>Image: Convection</span><span>Image: Conduction</span><span>Image: Radiation</span></span></span><span>Convection transfers heat energy through the air (and liquids). As the air heats up, the particles move further apart and become less dense, which causes the air to rise. Cooler air below moves in and heats up, creating a circular motion. The warm air circles and heats the room.</span><span>Conduction transfers heat energy through one substance to another when they are in direct contact. The moving molecules of a warm material can increase the energy of the molecules in a cooler material. Since particles are closer together, solids conduct heat better than liquids or gases.</span><span><span>Radiation is the heat that we feel coming from a hot object. It warms the air using heat waves (infrared waves) that radiate out from the hot object in all directions until it is absorbed by other objects. Transfer of heat byradiation travels at the speed of light and goes great distances.</span><span>With a log fire, the air in the room above the fire is heated and rises to create convection currents. The heat felt directly from the fire is transmitted to us through radiation. Conduction helps to keep a fire going by transferring heat energy directly from the wood to neighbouring wood in the fire</span></span></span>An effect of heat – expansion<span>When gases, liquids and solids are heated, they expand. As they cool, they contract or get smaller. The expansion of the gases and liquids is because the particles are moving around very fast when they are heated and are able to move further apart so they take up more room. If the gas or liquid is heated in a closed container, the particles collide with the sides of the container, and this causes pressure. The greater the number of collisions, the greater the pressure.</span><span>Sometimes when a house is on fire, the windows will explode outwards. This is because the air in the house has been heated and the excited molecules are moving at high speed around the room. They are pushing against the walls, ceiling, floor and windows. Because the windows are the weakest part of the house structure, they break and burst open, releasing the increased pressure.</span>
