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At what speed would one need to fire lead projectile in order for its temperature to rise from 22.7 '€ to 35.7 -C upon impact with stationary object? (Th...

Question

At what speed would one need to fire lead projectile in order for its temperature to rise from 22.7 '€ to 35.7 -C upon impact with stationary object? (The specific heat capacity of lead is 130 Jlkg-K.)

At what speed would one need to fire lead projectile in order for its temperature to rise from 22.7 '€ to 35.7 -C upon impact with stationary object? (The specific heat capacity of lead is 130 Jlkg-K.)



Answers

What must the initial speed of a lead bullet be at a temperature of $25.0^{\circ} \mathrm{C}$ so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows from the bullet to its surroundings. (Typical rifles have muzzle speeds that exceed the speed of sound in air, which is 347 $\mathrm{m} / \mathrm{s}$ at $25.0^{\circ} \mathrm{C}.)$

So here we're trying to essentially find the initial velocity of the bullet. So we know that the change in kinetic energy equals the total thermal energy that is transferred. So we can say that negative 1/2 the final squared minus V initial squared equals see Delta T plus the latent heat of formation. So we can say that of the final squared is going to be zero and the masses air canceling out. So we know that the initial velocity simply equals two times the specific heat times that change in temperature, plus the latent heat of formation to the 1/2 power. And so this rather we can just say this is equally two times the specific heat of lead. So this will be 130 Jules per kilogram per degree, Celsius times 327.3 degrees Celsius. That would be the melting temperature of lead minus 25 degrees Celsius and then plus the latent heat of formation of lead. So that'll be 24 2,500 Jules per kilogram, all again to the 1/2 power. So all of us to the 1/2 power and then the initial will equal 357.2 meters per second. So in order for this to melt so the in order for the bullet to completely melt the initial the lot firing velocity should be equal to 357.2 meters per second, which is well is within the range for a gun. That is the end of the solution. Thank you for watching.

Cinnamon 98. In this question, the moss off the bullet is given a 0.2 cages. The latent heat of fusion off lead is 23,000 jewels for K G, the melting temperature off the latest street, or be 7.5 degrees since years. The bullet was initially at 87 degrees Celsius, so that change in temperature that that is to 40.5 Calvins and the specific heat off lead is 120 year Jules Park Yogi Calvin. No, since the bullet is already at the G seven degrees Celsius, so we require its can take energy to raise the temperature of the bullet treat on the same 0.5 degrees Celsius. Then we also require energy to melt a bullet. So we get night the net can etiquette energy off the bullet half. Um, the spot is acquittal. M. C. There is not be less, um, substituting the values, uh, in the 0.2 These are is it called Oh, 0.2 Indo one. Wouldn't be it Indoor. 2 40 Foreign fire less zero. Pardon cereal to in tow 23,000. This will give us 0.1 The Esquire is equal to run Tzeitel 75 six said They still give us the initial we lost three off. The bullet is equal to 300. Don't be it. Meet their parts again.

My friends, This is a problem based on convergent up mechanical energy. Oh, and two he he'll be required. Bullet lead bullet is moving with velocity when brought to rest. Then it gets melted. So we have to find that be not that is half and the not physical to amount of the hip required to make it. That is, um CD a tragic plus m two l. So we not you will get twice of C. The 30 plus toys of letting t top melting. No substitute The widow group specifically top blood is 1 28. Melting point is 3273. Initial temperature is 30. Latent heat of vaporization is 2.32 Tend to leave power four. Yeah, you know, Sorry. We can't keep confusion. So on solving it you will get initial velocity of the bullet should be 3 50 m per second. That's thanks for watching it

In this problem, we're going to talk about heat. So remember that the heat necessary to raise an object to raise temperature oven object that has a mess and and a specific heat see by a temperature dumped a T is M C Delta T. Also, remember that foreign object to change its phase of matter. The necessary is the latent heat on. Remember that an object changes its phase of matter in a constant temperature, So the heat that's necessary to change the face of matter is m times the latent. Yeah, now, in our problem, we have to calculate what is the speed that a lead boat should have such that it would melt only do to its speed when it halted That I'm sorry only due to its kinetic energy went and holder eso basically consider that we have a bullet that has a mess and and the bullet is made of lead, and there are some things we need to consider here First. The specific heat see of the lad is 129 joules per kilogram degrees Celsius and the latent heat off mounting. The melting latent heat off the lead is about 2.3 times sent to the fore. Jules for killer. Also exercise tells us that initially the lad is that a temperature of 2030 degrees Celsius and given this are goes to calculate. So consider that the latter is moving with a certain kinetic energy, and then it suddenly stops and all the kinetic energy is converted into heat so that he que is equal to the kinetic energy MV squared over two. Now we want the lad to melt, so there are two components to our heat. Cute. There is the necessary to raise the temperature of the lad to the melting point, and the melting point of the lad is 327 point five degrees Celsius, plus the latent heat necessary to melt the lead. At this temperature, which is enough, this is M V squared over two so the EMS can cancel out the V be isolated, so V is the square root off two times. See Delta t plus out. So V is the square root of two times. See, that's the specific heat of the lead. 129 Jews frantically Celsius. Time is down to T and that is 327 0.5 degrees Celsius minus 30 degrees Celsius plus Mullah compete, which is 2.3 times sent to the fourth. This is in kilograms. I'm sorry. This is Jules. So we is equal to 350 m per second. And this is the answer to work.


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