Kinetic energy is not integral sum of momentum.. Then how u did this?phasacs said:K= ∫mvdv = ∫m dx/dt dv = ∫m dx/dv dv/dt dv = ∫m dv/dt dx = ∫Fdx = U
=> K=U, why isn't this true? If it is, wouldn't that mean that Kinetic Energy is always equal to Potential Energy?
How he found kinetic energy in terms of integral sum of momentum?? Can you explain sir?Orodruin said:The force is -dU/dx, not dU/dx. Furthermore, the potential is only defined up to an arbitrary constant. If you account for these things, what you get is just the work-energy theorem.
Isn't it the "change" in KE as nasu said earlier?STAR GIRL said:How he found kinetic energy in terms of integral sum of momentum??
Oh I seecnh1995 said:Isn't it the "change" in KE as nasu said earlier?
kinetic energy E=(1/2)*mv2
You can see dE/dv=mv.
So, dE=mv*dv.
phasacs said:K= ∫mvdv = ∫m dx/dt dv = ∫m dx/dv dv/dt dv = ∫m dv/dt dx = ∫Fdx = U
=> K=U, why isn't this true? If it is, wouldn't that mean that Kinetic Energy is always equal to Potential Energy?
Kinetic energy and potential energy are two different forms of energy that are often found in a system. Kinetic energy is associated with the motion of an object, while potential energy is associated with the position or configuration of an object. These two forms of energy are not always equal because they depend on different factors and can change independently of each other.
The difference between kinetic energy and potential energy can be affected by various factors such as the mass of an object, its velocity, its height, and the force acting on it. For example, an object with a larger mass will have more potential energy due to its greater gravitational pull, while an object with a higher velocity will have more kinetic energy due to its greater speed.
Yes, there are some cases where kinetic energy and potential energy can be equal. For example, if an object is at the highest point of its trajectory, it will have no kinetic energy but only potential energy. Similarly, if an object is at rest on the ground, it will have no potential energy but only kinetic energy. In these cases, the total energy of the system (kinetic energy + potential energy) remains constant.
The Law of Conservation of Energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. This law explains that the total energy of a system remains constant, but the forms of energy within the system can change. In the case of kinetic and potential energy, the sum of these two energies remains the same, but they can change independently of each other.
There are many real-life examples that demonstrate the difference between kinetic energy and potential energy. Some common examples include a rollercoaster at the top of a hill (high potential energy), a car driving down a hill (potential energy being converted to kinetic energy), a pendulum at its highest point (potential energy), and a swinging pendulum at its lowest point (kinetic energy). Understanding the difference between these two forms of energy is important in many fields of science, such as physics and engineering.