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PrudensOptimus
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Can someone distribute their knowledge of the above topics? I have a test on these tomorrow.
Thanks.
Thanks.
I'm assuming that you mean you tried to use the integrate idea to find work. Don't forget that force is a vector, so it is a dot product of the force with the displacement. Also, one subtle issue, work is <i>usually</i> associated with a particular force (i.e. friction), not the resultant, so you usually will not have that summation in the integrand. I'm really sorry, but I don't quite follow what you are trying to do.Originally posted by PrudensOptimus
I tried to integrate Work, ∫ΣF dx, where x is displacement, replacing F with ma, I end up getting δKE∫1/dx dx.
You probably use this notion when you are considering the work being done by the potential energy in the problem. If you include the potential energy in the problem, then the system is conservative. If you define the system without the potential energy (i.e. call gravity an external force), then the system is not conservative.Originally posted by PrudensOptimus
When do you use Wnet = ΔKE?
I saw some questions where W = ΔKE + ΔPE.
Or was that just for non conservative works? If it is for non conservative works only, then that means in cases when W = ΔKE, the W must mean for conservative?
It looks like they are using the subscript, "NC," to indicate that they are strictly talking about "Non-Conservative" work. That means that there is no potential energy that you can associate with it. Friction, I'm pretty sure, will contribute to the WNC. Gravity, and spring force stuff, goes into the ΔPE on the right.Originally posted by PrudensOptimus
What does it mean:
"It must be emphasized that all the forces acting on a body must be included in equation 6-10 either in the potential energy term on the right (if it is a conservative force), or in the work term WNC, on the left(but not in both!)"
EQ 6-10 : WNC = ΔKE + Δ PE.
Originally posted by turin
I'm assuming that you mean you tried to use the integrate idea to find work. Don't forget that force is a vector, so it is a dot product of the force with the displacement. Also, one subtle issue, work is <i>usually</i> associated with a particular force (i.e. friction), not the resultant, so you usually will not have that summation in the integrand. I'm really sorry, but I don't quite follow what you are trying to do.
Is this what you were trying to do?
∫Fdx = ∫madx = m∫(dv/dt)dx = m∫(dv/dx)(dx/dt)dx
= m∫(dv/dx)vdx = m∫vdv = (m/2)[v2 - v02] = KE - KE0 = ΔKE
F is the integrand, and it can be a function of the position of the particle, in general. If you replace it by ma, then the a must be a function of the position of the particle, in general. You cannot replace this by a constant, in general.Originally posted by PrudensOptimus
When I replaced F with ma, and a with (v^2 - v0^2)/2Δx, isn't m((v^2 - v0^2)/2) suppose to be treated as constants?
This is the chain rule in action:Originally posted by PrudensOptimus
mç(dv/dx)vdx --- how did you get to that part?
Work is the measure of the force applied to an object over a certain distance, while energy is the ability of an object to do work. In other words, work is the action that results in a change in energy.
Power is the rate at which work is done or energy is transferred. It is equal to the amount of work divided by the time it takes to do the work. In other words, power measures how quickly an object can do work or transfer energy.
Momentum is a measure of an object's motion and is equal to the product of its mass and velocity. It is related to work and energy through the principle of conservation of momentum, which states that the total momentum of a system remains constant unless an external force acts on it.
These concepts have wide applications in various fields such as physics, engineering, and even everyday life. For example, understanding the principles of work and energy is crucial in designing efficient machines and structures, while power is important in determining the performance of engines and motors. Momentum is also important in sports and transportation, as it affects the movement and speed of objects.
Conserving work, energy, power, and momentum is important in order to ensure the efficient use of resources and to minimize waste. This can be achieved by reducing friction and other forms of energy loss, using renewable energy sources, and designing systems that can transfer and store energy efficiently.