How do I set up equations for a mass connected to a wall by a spring and a damping pot, which then has a force applied to it?
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How do I set up equations for a mass connected to a wall by a spring and a damping pot, which then has a force applied to it?
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- A plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.Discuss the modes of heat transfer that determine the equilibrium temperature of the space shuttle Endeavour when it is in orbit. What happens when it reenters the earths atmosphere?A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.
- 2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5.1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other)2) What are the matrices K and M for the system?3) What are the normal frequencies of the system?4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?A metallic container of fixed volume of 2.5 × 10−3 m3 immersed in a large tank of temperature 27 °C contains two compartments separated by a freely movable wall. Initially, the wall is kept in place by a stopper so that there are 0.02 mol of the nitrogen gas on one side and 0.03 mol of the oxygen gas on the other side, each occupying half the volume. When the stopper is removed, the wall moves and comes to a final position. The movement of the wall is controlled so that the wall moves in infinitesimal quasi-static steps. (a) Find the final volumes of the two sides assuming the ideal gas behavior for the two gases. (b) How much work does each gas do on the other? (c) What is the change in the internal energy of each gas? (d) Find the amount of heat that enters or leaves each gas.
- Air is trapped in the piston in the cylinder. A spring is connected to the upper portion of the piston and returns the force upon compression by the F = -kx equation. k = 50,000 N/m and x is the distance traveled when the piston is compressed. The piston is located 10 cm above the bottom of the cylinder with a cross-sectional area of 0.01 m2 and an initial condition of 1 bar and 25°C. In this state, the spring does not apply force to the piston. At this time, the system was reversibly heated and the temperature rose to 100°C. (a) What happened was (b) What is the heat transferred?hi, can you solve this ? The temperature of the engine of an armored personnel carrier returning from an exercise from 100 ° C drops to 80 ° C after 10 minutes in an environment where the air temperature is 20 ° C. What will the engine temperature be after 40 minutes?How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.
- A body is removed from a confined space where the temperature is 70°C and is taken outside, where the air temperature is 10°C. After one-half minute, the body's temperature is read as 50°C. How long will it take for the body's temperature to reach 15°C? What is the value of the proportionality constant?Solar heating of a house is much more efficientif there is a way to store the thermal energy collected during theday to warm the house at night. Suppose one solar-heated homeutilizes a concrete slab of area 12 m2and 25 cm thick. (a) If thedensity of concrete is 2400 kg>m3, what is the mass of the slab?(b) The slab is exposed to sunlight and absorbs energy at a rate of1.4 * 107J>h for 10 h. If it begins the day at 22 °C and has a specificheat of 750 J>1kg # K2, what is its temperature at sunset? (c) Modelthe concrete slab as being surrounded on both sides (contact area24 m2) with a 2.0-m-thick layer of air in contact with a surface thatis 5.0 °C cooler than the concrete. At sunset, what is the rate atwhich the concrete loses thermal energy by conduction throughthe air layer? (d) Model the concrete slab as having a surface areaof 24 m2and surrounded by an environment 5.0 °C cooler thanthe concrete. If its emissivity is 0.94, what is the rate at which theconcrete loses thermal…Hi, can you help me with the following problem? A thermally insulated tank of water 2 m x 2 m, depth 1 m is stirred with a paddle for threehours. If the paddle is driven by a motor whose shaft power is 8 kW determine the rate ofchange of temperature in degrees C per hr and the increase in temperature of the water.The specific heat of water is 4200 J/kgC. Identify a system and start your analysis from anappropriate form of the Fist Law of Thermodynamics