- #1
ZGMF - X20A
- 8
- 0
I just want to know in what conditions does mgh = 1/2mv^2 when a guy goes down a slope and in what conditions does mgh =/= 1/2mv^2. Thanks in advance.
Understanding Mgh = 1/2mv^2: Conditions for Equal and Unequal Energy on Slopes
- Thread starter ZGMF - X20A
- Start date
In summary, the conversation discusses the conditions in which the equation mgh = 1/2mv^2 applies when an object goes down a slope. The principle of conservation of energy is also mentioned, where the initial potential energy (PE) and kinetic energy (KE) of an object must equal the final PE and KE. It is suggested that using the equation for change in PE = -change in KE is more accurate, and that energy is only conserved when there are no non-conservative forces, such as friction. In the case of friction, the increase in KE is less than the decrease in PE due to energy being lost to the surroundings.
- #2
semc
- 368
- 5
according to COE, (initial)PE + KE = PE + KE(final) so i think that its better to use this instead of your equation.For example,if the object were to be released with some initial velocity,the KE(initial) would not be 0 so total initial energy is mgh+1/2mv^2 instead of mgh.Btw,it is more precise to write change of PE = -change of KE as this shows that energy is conserved.
- #3
HallsofIvy
Science Advisor
Homework Helper
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And energy is conserved as long as the are no "non-conservative" forces- i.e. as long as there is no friction.
- #4
ZGMF - X20A
- 8
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So when there is no friction P.E = K.E?
- #5
Tomsk
- 227
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Yes, decrease in PE= increase in KE and vice versa. If there's friction, decrease in PE= increase in KE + energy 'lost' to surroundings, so increase in KE<decrease in PE.
FAQ: Understanding Mgh = 1/2mv^2: Conditions for Equal and Unequal Energy on Slopes
What is the meaning of the equation "Mgh = 1/2mv^2"?
The equation "Mgh = 1/2mv^2" is known as the Law of Conservation of Energy. It states that the total mechanical energy of a system, consisting of potential energy (Mgh) and kinetic energy (1/2mv^2), remains constant as long as there is no external forces acting on the system.
What do the variables M, g, h, m, and v represent in the equation?
M represents the mass of the object, g represents the acceleration due to gravity, h represents the height of the object, m represents the mass of the object in motion, and v represents the velocity of the object.
How is the equation "Mgh = 1/2mv^2" used in real-life scenarios?
This equation is commonly used in physics to calculate the potential and kinetic energy of objects. It is also used in engineering to design structures and machines that involve energy transfer and conservation.
What is the significance of the factor 1/2 in the equation?
The factor 1/2 is used to represent the relationship between potential and kinetic energy. It signifies that the kinetic energy of an object is half of its potential energy at a given point.
How is the equation "Mgh = 1/2mv^2" related to the concept of work?
The equation "Mgh = 1/2mv^2" is derived from the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. This means that the work done on an object by a force is converted into the object's kinetic energy, according to the equation.