An electric heater of 500 watts works on 250V. What is the resistance?
First, in order to have Power = 500W at 250 Volts, we need 2 Amps of current flow. (P = V x I)Second, in order to have I = 2A with V = 250V, we need R = V/I = 125 Ohms. Same answer as many of the others. But this is true only for the steady state, while the heater element is hot. Before it heats up, the heater element will have a somewhat lower resistance, maybe 100 ohms or less. (Resistance increases with temperature.)Measure the heater element’s resistance with an ohmmeter (while it’s at room/ambient temperature), and you will definitely see less than 125 ohms. This means that it draws more current (and thus more power) while the element heats up to its steady state temperature.
Suppose the clean water of a stream flows into Lake Alpha?
Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow for each lake is 500 liters per hour. Lake Alpha contains 500 thousand liters of water, and Lake Beta contains 400 thousand liters of water. A truck with 500 kilograms of Kool-Aid drink mix crashes into Lake Alpha. Assume that the water is being continually mixed perfectly by the stream. Let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. Find a formula for the incremental change in the amount of Kool-Aid, Δx, in terms of the amount of Kool-Aid in the lake x and the incremental change in time Δt. Enter Δt as Deltat. Δx= kg Find a formula for the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. x(t)= kg Let y be the amount of Kool-Aid, in kilograms, in Lake Beta t hours after the crash. Find a formula for the incremental change in the amount of Kool-Aid, Δy, in terms of the amounts x,y, and the incremental change in time Δt. Enter Δt as Deltat. Δy= kg Find a formula for the amount of Kool-Aid in Lake Beta t hours after the crash. y(t)= kg
A hole is made at the bottom of the tank filled with water. if the total pressure at the bottom is 3 atmospheres, then what is the velocity of efflux?
you can apply Bernoulli’s equation to get the velocity. the dynamic pressure is 2 atmosphere. sov=sqrt(2*2*101325/1000)=20.13 m/sec
A solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder are released from the top of an inclined plane. Which object arrives first?
We need to assume that each object has uniform density and that they all roll without slipping. Perhaps surprisingly size, mass, density height don’t matter. Definemass [math]=m[/math]initial height [math]=h[/math]gravity [math]=g[/math]final velocity [math]=v[/math]radius [math]=r[/math]angular velocity [math]= \omega=\frac{v}{r}[/math]moment of inertia [math]=I=kmr^2[/math] (where [math]k[/math] is a measure how close to the edge the mass is, on average)Then by conservation of energy,[math]mgh=\frac12 m v^2 +\frac12 I \omega^2 [/math][math]2gh= v^2 + k v^2 [/math][math]v=\sqrt{\dfrac{2gh}{1+k}}[/math]So to maximize [math]v[/math] we need to minimize [math]k[/math] - in other words we want the mass to be concentrated as close to the centre as possible. This is intuitive, we don’t want to ‘waste’ energy spinning up the object - we want to concentrate on maximizing its speed.Therefore the slowest object will be the hollow cylinder (all the mass is at the edge) and the fastest will be the solid sphere.
Linear Differential Equations - Concentration as a function of time?
Suppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows into the second lake, and then water from the second lake flows further downstream. The in and out flow from each lake is 500 liters per hour. The first lake contains 100 thousand liters of water and the second lake contains 200 thousand liters of water. A truck with 500 kg of toxic substance crashes into the first lake. Assume that the water is being continually mixed perfectly by the stream. a) Find the concentration of toxic substance as a function of time in both lakes. b) When will the concentration in the first lake be below 0.001 kg per liter? c) When will the concentration in the second lake be maximal? I'm really stuck on how to start this let alone complete it, any help would be much appreciated :) thank youuuu!