A 74 kg skier is pulled 50 meters up a 30 degree incline. How much work is required to pull the skier up?
I will be happy to critique your thinking. Think about the height she went up.
To calculate the work required to pull the skier up the incline, we need to use the formula:
Work = Force × Distance × Cos(θ)
Where:
- Force is the component of force acting along the direction of motion, which in this case is the weight of the skier.
- Distance is the displacement of the skier, which is given as 50 meters.
- θ is the angle between the direction of motion and the force vector, which is 30 degrees in this case.
First, let's calculate the force acting along the incline. The force acting on the skier is its weight, which can be calculated using the equation:
Weight = mass × gravity
Given the mass of the skier is 74 kg, and assuming the acceleration due to gravity is 9.8 m/s², we can calculate:
Weight = 74 kg × 9.8 m/s² = 725.2 N
Next, we need to calculate the component of the weight vector along the incline. This can be found using trigonometry, as shown:
Force along incline = Weight × Sin(θ)
Force along incline = 725.2 N × Sin(30°) ≈ 362.6 N
Finally, we can calculate the work using the formula mentioned earlier:
Work = Force × Distance × Cos(θ)
Work = 362.6 N × 50 m × Cos(30°)
Calculating further:
Work = 362.6 N × 50 m × 0.866
Work ≈ 15,629 Joules
Therefore, approximately 15,629 Joules of work is required to pull the skier up the 30-degree incline.