A man cycles up a hill whose slope is 1in20. If themass of the man and the cycle is 150kg and the man covers a distance of 100m along the incline, calculate the work done by theman.
sinα=1/20=0.05
sinα=h/s => h=s•sinα
W=ΔPE=m•g•h=(m₁+m₂)•g•s•sinα=..
To calculate the work done by the man while cycling up the hill, we need to use the formula:
Work = Force * Distance * cosθ
Here's how to calculate it step by step:
1. Calculate the force exerted by the man against gravity:
Force = mass * acceleration due to gravity = 150 kg * 9.8 m/s²
2. Calculate the angle of the hill slope:
Slope = 1 in 20 = 1/20 = 0.05
Angle (θ) = arctan(0.05)
3. Convert the angle from radians to degrees (optional):
Angle in degrees = θ * (180/π)
4. Calculate the distance along the incline:
Given distance = 100 m
5. Calculate the cosine of the angle:
cosθ = cos(angle in radians)
Now, plug in the values into the work formula:
Work = Force * Distance * cosθ
Simply substitute the values we calculated into the formula and solve for work:
Work = (150 kg * 9.8 m/s²) * 100 m * cosθ
After substituting, you'll have the work done by the man while cycling up the hill.