Question

Morning breakfast gives 5000 cal to a 60Kg person. The efficiency of a person is $30\%$. The height up to which the person can climb up by using energy obtained from breakfast is:
A. $5m$
B. $10.5m$
C. $15m$
D. $16.5m$

Answer 1

No machine or no person can be hundred percent efficient. The amount of energy is taken through the food incase of humans or fuel in case machines cannot be utilized totally. Some proportion is always lost either through heat or body waste or through evaporation losses in the case of fuel. So the ratio of the amount of energy used to the amount of energy taken is called efficiency.
Formula used:
$W = mgh$

Complete step-by-step solution:
Humans usually get energy for their daily work through food intake. The carbohydrates which are present in the food will be converted into glucose inside the body and stored as ATP i.e adenosine triphosphate. Whenever energy is required that ATP will break into ADP i.e adenosine diphosphate and energy.
So now a person has got 5000 calories of energy through his breakfast intake. His energy conversion efficiency is given as 30 percent.
So first we should convert this energy into SI units that are into joules. The energy available for usage is thirty percent of total energy.
\eqalign{ & E = \dfrac{{30}}{{100}} \times 5000 \cr & \Rightarrow E = 1500cal \cr}
Now let us convert these calories into joules.
$1cal = 4.2J$
$\Rightarrow 1500cal = 1500 \times 4.2 = 6300J$
This energy will be available for a person to climb the hill.
$W = mgh$ where ‘W’ is the work to be done to climb the hill which will be equal to energy present for usage. ‘m’ is the mass of the person and ‘g’ is the acceleration due to gravity and ‘h’ is the height climbed.
$W = mgh$
\eqalign{ & \Rightarrow 6300 = 60 \times 10 \times h \cr & \Rightarrow h = \dfrac{{6300}}{{600}} \cr & \Rightarrow h = 10.5m \cr}
So that person can climb a hill of height 10.5 meter.
Hence option B will be the answer.

Note: Here a man will be moving up that means he will be moving against the gravity. When we are overcoming a force and going against it that definitely means some work to be done to overcome that force. Let us assume a case is coming down, then no work needs to be done as gravity will help him but he will gain some kinetic energy due to this.