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| Newton's third law problem. |
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| electrodacus:
--- Quote from: Kleinstein on December 08, 2022, 06:58:26 pm ---No : to accerate the 10 ton vehicle to 0.1 m/s in 0.1 seconds it needs way more force: the accelration is dV/dt and F = m *A = 10000 kg * 0.1m/s / 0.1 s = 10000 N. That is well more than 60 N you calculated for the drag force. The assumption of 100% efficiency for the wind is wrong. --- End quote --- Keep in mind this is a theoretical problem so there is no rolling resistance. The vehicle barely moved in that 0.1s and the 0.11m/s is not much KEvehicle = 0.5 * 10000kg * (0.11m/s)2 = 60 Joules Yes the assumption of 100% efficiency for a theoretical sail is correct. And even in real world that will still be around the same. What happened in this setup is that about 1m3 of air collides with the 1m2 sail and transfers all that kinetic energy to vehicle. KEair = 0.5 * 1.2kg * (10m/s)2 = 60 Joules In that 0.1s just 1 cubic meter of air can collide with the vehicle body. Do not ignore the conservation of energy when solving any problem. Here the mistake is to not consider air made out of particles that have elastic collisions with vehicle body. You do that for calculating drag force but then you want to ignore that when calculating power needed to overcome drag. Even to travel 1m the vehicle will require less than 10 seconds assuming you remove the sail after the first 100ms and there will be no extra energy loss or gain so still the same 60 Joules of vehicle stored kinetic energy. |
| Kleinstein:
--- Quote from: electrodacus on December 08, 2022, 07:46:58 pm --- Do not ignore the conservation of energy when solving any problem. Here the mistake is to not consider air made out of particles that have elastic collisions with vehicle body. You do that for calculating drag force but then you want to ignore that when calculating power needed to overcome drag. --- End quote --- The conservation of energy is OK, but than you have to also include the friction in the air, converting kinetic energy of the wind to heat. In this case it just not very practical to use conservation of energy as the starting point. It is much easier to use the drag force and the basic newton's laws. To drive against the wind, the vehicle has to overcome the drag force. So it does not matter if the force is from a large sail in low wind or small sail in high wind. In a though experiment the wheel / motor part does not even know if the force is from wind or electromagnetic or friction to the ground. The ideallized sail may theoretical approach 100% efficiency - but only when moving at nearly the speed of the wind. Going at 10% the speed of the wind it is more like 10% efficient. With wind resistance there is not 100% transfer of kinetic energy. Generally much of the ernergy is converted to heat. The collisions are not 100% elastic - that is only an approximation sometimes used in some simplified calculations. Fast flying planes do get hot from the air resistance. |
| electrodacus:
--- Quote from: Kleinstein on December 08, 2022, 08:17:15 pm ---The conservation of energy is OK, but than you have to also include the friction in the air, converting kinetic energy of the wind to heat. In this case it just not very practical to use conservation of energy as the starting point. It is much easier to use the drag force and the basic newton's laws. To drive against the wind, the vehicle has to overcome the drag force. So it does not matter if the force is from a large sail in low wind or small sail in high wind. In a though experiment the wheel / motor part does not even know if the force is from wind or electromagnetic or friction to the ground. The ideallized sail may theoretical approach 100% efficiency - but only when moving at nearly the speed of the wind. Going at 10% the speed of the wind it is more like 10% efficient. With wind resistance there is not 100% transfer of kinetic energy. Generally much of the ernergy is converted to heat. The collisions are not 100% elastic - that is only an approximation sometimes used in some simplified calculations. Fast flying planes do get hot from the air resistance. --- End quote --- Air is not an ideal gas but close enough in relation to how much of his kinetic energy is transferred to the vehicle. There is really no difference between vehicle colliding with stationary air particles (no wind) and moving air particles colliding with a stationary vehicle. If you change the reference frame the result will need to be exactly the same else mistakes were made. The sail size vs wind speed is relevant. Say you want the same 60N at just 5m/s instead of 10m/s wind. Then your sail size will need to be 4x larger so 4m2 instead of just 1m2 needed with 10m/s wind. But then the power available is 2x lower than before even if force is the same. Fd = 0.5 * 1.2 * 1 * (10)2 = 60N Fd = 0.5 * 1.2 * 4 * (5)2 =60N Pd = Fd * 10 = 600W Pd = Fd * 5 = 300W If you want the same power at half the wind speed you need 8x the sail area. The wind speed is relevant not just the force. You will not make this assumptions if you considered the vehicle powered by ideal collisions with large balls that you can see. It is the same thing just that air is made out of super small (low weight) particles even different size that collide almost perfectly elastic with the vehicle body. |
| Kleinstein:
The collisions for the molecules with a solid are not really elastic. One sees this as heat can be exchanges from a gas and solid. Even of only small fraction of the energy is lost to heat, the argumet with energy conservation breaks down and should be avoided. At best it is a weak argument - so one of the first points to question. There is no physical law of conservation of kinetic energy. There is hower conservation of momentum and thus a balance of force. The assumption of conservation of kinetic energy is a rather weak one - it can work for explite eleastic collisions or frictionless ideallized mechnical systems. However it does not work for systems with friction - air resistance is a type of friction. The picture of moving particles is not really practical to understand air resistance. It is not a transfer of kinetic energy to kinetic energy (most of the energy in the gas is thermal energy and the wind is more like a minor shift in the distribution). The interaction is more like a transfer of momentum and force. Much of the air particels never actuall hit the obstacle but hit other air that diverts it to the sides and can create turbulance that than dissipates the energy away from the obstacle. |
| electrodacus:
--- Quote from: Kleinstein on December 08, 2022, 09:59:52 pm ---The collisions for the molecules with a solid are not really elastic. One sees this as heat can be exchanges from a gas and solid. Even of only small fraction of the energy is lost to heat, the argumet with energy conservation breaks down and should be avoided. At best it is a weak argument - so one of the first points to question. There is no physical law of conservation of kinetic energy. There is hower conservation of momentum and thus a balance of force. The assumption of conservation of kinetic energy is a rather weak one - it can work for explite eleastic collisions or frictionless ideallized mechnical systems. However it does not work for systems with friction - air resistance is a type of friction. The picture of moving particles is not really practical to understand air resistance. It is not a transfer of kinetic energy to kinetic energy (most of the energy in the gas is thermal energy and the wind is more like a minor shift in the distribution). The interaction is more like a transfer of momentum and force. Much of the air particels never actuall hit the obstacle but hit other air that diverts it to the sides and can create turbulance that than dissipates the energy away from the obstacle. --- End quote --- Understanding what air is and how it interacts with the vehicle is actually key to understanding this problems. With no wind you seem to agree with the fact that all that is there are elastic collisions but then when air moves you try to find some alternative explanation and that is not the case as all that changed is the frame of reference. If you take the example of the 1m2 frontal area and coefficient of drag of 1 traveling through air at 10m/s Then you will say drag force is 60N and power needed to overcome this drag is 600W If the same vehicle travels at half this speed you again will say drag force is 15N and power deeded to overcome drag is 75W So all that changed is the vehicle speed trough stationary air and reducing the speed to half reduced the drag force 4x but reduced the power by 8x If you look at what happens and the fact that each second vehicle collides with 10 cubic meters of air when driving at 10m/s and collides with 5 cubic meters when driving at 5m/s When you calculate the collision energy you get a perfect transfer of energy like ideal elastic collisions took place. But then if air moves instead of vehicle you want to claim that is no longer the same thing when nothing has actually charged other than the frame of reference. You are not using different equations for drag force but you insist on two different equations for drag power. Is likely just based on the wrong intuition of what happens. |
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