Finding Mechanical Energy without knowing Efficiency

In summary, the man expended 727.2 kcal during his hike, but the Mechanical Energy (useful work energy) expended for this hike was the change in gravitational potential, or PE = mgh, which is equal to the energy required to lift his mass up the mountain.
  • #1
jennyskywalker
3
0

Homework Statement


A 65 kg man goes for a 72 minute hike up a mountain that is 400.0 metres in vertical height. The energy consumption rate for this climb is 10.1 kcal/min. What is the Mechanical Energy (useful work energy) expended for this hike? (in kcal)


Homework Equations


ME= (Efficiency x Eout)/100

The Attempt at a Solution


10.1 x 72 = 727.2 (Therefore Eout=727.2) But I don't know the efficiency! So how do I figure this out?
 
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  • #2
How much energy must the man expend to lift his mass up the mountain?
 
  • #3
SteamKing said:
How much energy must the man expend to lift his mass up the mountain?

727.2 kcal? But that is the total energy expended, including heat energy. ME=(efficiency x 727.2)/100. That's all I know!
 
  • #4
I asked on another forum, and they said ME= mgh, but according to my teacher, PE (potential energy)=mgh, and I'm looking for Mechanical energy!
 
  • #5
energy is energy.

The man expended so many kcal thru his metabolism while walking up the hill. That you have calculated.

However, in moving his mass up the hill, a certain portion of this energy was consumed in moving his mass up the hill against gravity. This energy is equal to the change in gravitational potential from the bottom of the hill to the top.
 

FAQ: Finding Mechanical Energy without knowing Efficiency

How do I calculate mechanical energy without knowing efficiency?

To calculate mechanical energy without knowing efficiency, you can use the formula: Mechanical Energy = Kinetic Energy + Potential Energy. Kinetic energy is calculated by mass x velocity^2 / 2, while potential energy is calculated by mass x gravity x height. Efficiency is not needed in this calculation since it only affects the amount of work output, not the total mechanical energy.

Can mechanical energy be negative if efficiency is not known?

Yes, mechanical energy can be negative even without knowing efficiency. This can happen if the kinetic energy and potential energy have opposite signs, such as when an object is moving in the negative direction and has a negative potential energy due to its position.

Is mechanical energy the same as work?

No, mechanical energy and work are not the same. Mechanical energy is the sum of kinetic and potential energy, while work is the measure of energy transferred when a force is applied to an object and it moves a certain distance. Efficiency affects the amount of work done, but not the total mechanical energy.

Can efficiency be calculated if mechanical energy is known?

Yes, efficiency can be calculated if mechanical energy is known. The formula for efficiency is work output / work input, or (mechanical energy output - mechanical energy input) / mechanical energy input. By knowing the mechanical energy input and output, you can calculate the efficiency.

How does mechanical energy affect the performance of a machine?

Mechanical energy is a measure of the total energy of a system, and it affects the performance of a machine by determining the amount of work that can be done. The higher the mechanical energy, the more work can be done by a machine. However, the efficiency of a machine also plays a role in its performance, as a machine with a higher efficiency can convert more of its input energy into useful work.

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