Work and Energy of a climbing person

N = \Delta PE = PE_{final} - PE_{initial} = 3000 Jand \Delta PE = (mg) \Delta hso for a mass of 837.558 N we get\Delta h = \frac{AMN}{mg} = \frac{3000J}{837.558N} = 3.583mWe have to convert 3.583m to feet:1m = 3.281 ftTherefore, 3.583m = 3.583m x 3.281ft/m = 11.745ft.In summary, a person weighing 188.3 lb would have to climb 11.745 feet to gain
  • #1
agadag
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0

Homework Statement



How many meters above the ground would a person ( 188.3 lb ) have to climb to gain 3 kilojoules ( 3000 joules ) of potential energy. We usually measure our weight ( W = mg ) in pounds. For conversions, you may need to know that 1 pound is equal to 4.448 Newtons.

Homework Equations



PE = MGH

The Attempt at a Solution


3000=837.558*9.8*h
I used this to solve for h...not working! please help!
 
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  • #2
agadag said:

Homework Statement



How many meters above the ground would a person ( 188.3 lb ) have to climb to gain 3 kilojoules ( 3000 joules ) of potential energy. We usually measure our weight ( W = mg ) in pounds. For conversions, you may need to know that 1 pound is equal to 4.448 Newtons.

Homework Equations



PE = MGH

The Attempt at a Solution


3000=837.558*9.8*h
I used this to solve for h...not working! please help!
PE = Work done against gravity = [itex]\vec F \cdot \vec d = (mg)h = [/itex] weight x height.

You do not have to use g explicitly here since you are given the weight, in Newtons, of one pound of matter. The person weighs 188.3 times that or, as you have found, 837.558 N.

AM
 
  • #3


I would first clarify the units being used in the problem. The weight of the person is given in pounds, but the conversion factor for pounds to Newtons is not needed in this problem. The mass of the person can be calculated by dividing the weight by the acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, the mass of the person is approximately 188.3 lb/4.448 N = 42.36 kg.

Next, I would use the equation for potential energy, PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Rearranging the equation to solve for h, we get h = PE/mg.

Substituting the values given in the problem, h = (3000 J)/(42.36 kg * 9.8 m/s^2) = 7.03 meters. Therefore, the person would have to climb 7.03 meters above the ground to gain 3 kilojoules of potential energy.
 

FAQ: Work and Energy of a climbing person

What is the relationship between work and energy in a climbing person?

The work-energy theorem states that the work done on an object equals the change in its kinetic energy. In the context of a climbing person, this means that the work done by the person's muscles is converted into kinetic energy, allowing the person to move up the climbing wall.

How does the weight of a climbing person affect their work and energy?

The weight of a climbing person affects their work and energy in two ways. First, the person must work against the force of gravity as they climb, which requires the expenditure of energy. Second, the person's weight also affects their potential energy, which is converted to kinetic energy as they climb up the wall.

What role does friction play in the work and energy of a climbing person?

Friction plays a crucial role in the work and energy of a climbing person. Friction between the person's hands and the climbing holds allows them to grip and pull themselves up the wall, performing work and converting their energy into potential and kinetic energy. Without friction, it would be impossible for a person to climb.

How does the angle of the climbing wall affect the work and energy of a climbing person?

The angle of the climbing wall affects the work and energy of a climbing person in two ways. First, a steeper wall requires the person to work against a greater force of gravity, increasing the amount of work and energy required to climb. Second, the angle of the wall also affects the person's potential and kinetic energy, as a steeper angle results in a greater change in height and velocity as the person climbs.

How do different climbing techniques affect the work and energy of a climbing person?

Different climbing techniques can affect the work and energy of a climbing person in various ways. For example, using efficient and precise movements can reduce the amount of work and energy required to climb. On the other hand, using brute force and inefficient movements can increase the work and energy expenditure. Additionally, using rest and recovery techniques can also affect the energy levels of a climbing person throughout a climb.

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