How much work does a 69 kg person do against gravity in walking up a trail that gains 790 m in elevation
M g H = 69 * 9.8 * 790 = ___ joules
534198
To calculate the work done by a person against gravity while walking up a trail, we need to use the formula:
Work = Force × Distance × Cos(θ)
Where:
- Force is the force exerted against gravity, which is equal to the person's weight (mass × acceleration due to gravity)
- Distance is the vertical distance (elevation) gained while walking up the trail
- θ represents the angle between the force vector (upward) and the displacement vector (vertical distance)
First, let's calculate the force exerted against gravity by the person:
Force = mass × acceleration due to gravity
Force = 69 kg × 9.8 m/s² (acceleration due to gravity is approximately 9.8 m/s²)
Force = 676.2 N
Next, let's calculate the work done against gravity:
Work = Force × Distance × Cos(θ)
Since we only have the vertical distance gained (790 m), the angle θ between force and displacement is 0 degrees (cosine of 0 degrees is 1).
Work = 676.2 N × 790 m × Cos(0°)
Work = 533,238 Joules
Therefore, a 69 kg person does approximately 533,238 Joules of work against gravity while walking up a trail that gains 790 m in elevation.