- #1
ZGMF - X20A
- 8
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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
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SUMMARY
The discussion clarifies the conditions under which the equation mgh = 1/2mv^2 holds true when an object descends a slope. It establishes that this equation applies only in the absence of non-conservative forces, such as friction. When friction is present, the relationship changes, as some potential energy is converted into thermal energy rather than kinetic energy. The conservation of energy principle is emphasized, stating that total mechanical energy remains constant only when no external forces do work on the system.
PREREQUISITES- Understanding of gravitational potential energy (PE = mgh)
- Familiarity with kinetic energy (KE = 1/2mv^2)
- Knowledge of the conservation of energy principle
- Concept of non-conservative forces, particularly friction
- Study the conservation of energy in mechanical systems
- Explore the effects of friction on energy transfer
- Learn about potential and kinetic energy transformations on inclined planes
- Investigate the role of non-conservative forces in energy dissipation
Physics students, educators, and anyone interested in understanding energy dynamics in mechanical systems, particularly in scenarios involving slopes and friction.
- #2
semc
- 364
- 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
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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
- 0
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.
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