Minimum work needed to climb to the top of a peak

• derpydashie6167
In summary: Work is done when the inner product of those vectors is positive. In this case, that means the force is pushing the climber up, and the displacement is going down.
derpydashie6167
Homework Statement
A 71.5-kg hiker starts at an elevation of 1300 m and climbs to the top of a peak 2680 m high. What is the minimum work required of the hiker?
Relevant Equations
w=(Fcos[theta])d
F=ma
PE=mgh
f=ma=71.5*9.8 = 700.7 I know this is not right because he is also going up against gravity but I don't know what else to use for acceleration. I don't know the angle but I assume it is a 90 degree cliff.
w = (Fcos90)1380 = 0. But zero is not the correct answer.

Last edited by a moderator:
The angle of the cliff does not matter. The angle theta is also not the angle of the cliff, it is the angle between the force applied and the path taken, and is thus definitely not 90 degrees. The work done is then the path integral of the inner product between the force applied and the displacement. However, in this particular case you don't need to know any of those. Think about how work and energy are related.

derpydashie6167 said:
Homework Statement:: A 71.5-kg hiker starts at an elevation of 1300 m and climbs to the top of a peak 2680 m high. What is the minimum work required of the hiker?
Relevant Equations:: w=(Fcos[theta])d
F=ma
PE=mgh

f=ma=71.5*9.8 = 700.7 I know this is not right because he is also going up against gravity but I don't know what else to use for acceleration. I don't know the angle but I assume it is a 90 degree cliff.
w = (Fcos90)1380 = 0. But zero is not the correct answer.
In my opinion this is a poorly stated problem, but I understand what its author wants you to do. You need to find the minimum work done by the climber against gravity. Presumably that is minimum when the climber's kinetic energy does not change as (s)he climbs. Does that help? Think work-energy theorem.

Also, you seem to have a serious misconception about work. If the cliff is vertical, that means a 90o angle with respect to the horizontal. Angle θ in the expression for work is the angle between the force and the displacement vectors. Do you see why that angle is not 90o?

What is the minimum work needed to climb to the top of a peak?

The minimum work needed to climb to the top of a peak depends on various factors such as the height and steepness of the peak, the physical fitness and experience of the climber, and the weather conditions. It is not a fixed value and can vary greatly from one peak to another.

How is the minimum work needed to climb to the top of a peak calculated?

The minimum work needed to climb to the top of a peak is calculated by taking into account the elevation gain, distance, and difficulty of the route. This calculation is often done using mathematical equations and formulas that consider the energy expenditure required for climbing at different angles and altitudes.

Does the weight of the climber affect the minimum work needed to climb to the top of a peak?

Yes, the weight of the climber does affect the minimum work needed to climb to the top of a peak. Heavier climbers may require more energy to ascend the same peak compared to lighter climbers, as they have to carry more weight with each step.

Can the minimum work needed to climb to the top of a peak be reduced?

Yes, the minimum work needed to climb to the top of a peak can be reduced by taking breaks, pacing oneself, and using efficient climbing techniques. Additionally, having a lighter pack and being physically fit can also help reduce the amount of work needed to climb a peak.

Is it possible to accurately predict the minimum work needed to climb to the top of a peak?

While it is possible to estimate the minimum work needed to climb to the top of a peak, it is not possible to accurately predict it. This is because there are many variables involved, such as the physical condition of the climber and the weather conditions, which can change at any time during the climb.

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