A baThe power developed by a man in riding up a 6 percent grade at a constane speed is 200 W the man and his bicycle have a combined mass of 80 kg.Determine the speed of rding
To determine the speed of riding, we first need to find the force exerted by the man and his bicycle to overcome the gravitational pull while riding up the 6 percent grade.
1. Calculate the force required to overcome the gravitational pull:
The force required to move against gravity can be calculated using the formula: F = m * g * sin(theta), where:
F is the force required,
m is the combined mass of the man and the bicycle (80 kg),
g is the acceleration due to gravity (9.8 m/s^2),
theta is the angle of the grade (6% or 0.06).
So, F = 80 kg * 9.8 m/s^2 * sin(0.06).
2. Calculate the work done by the man and his bicycle:
The work done to ride up the grade can be calculated using the formula: W = F * d, where:
W is the work done (equal to the power developed, 200 W),
F is the force required (found in step 1),
d is the distance traveled.
3. Calculate the distance traveled:
Since the speed is constant, we can assume it represents a steady state. In this case, we can use the equation: W = F * d = m * g * d * sin(0.06), where:
W is the work done (200 W),
F is the force required (found in step 1),
m is the combined mass of the man and the bicycle (80 kg),
g is the acceleration due to gravity (9.8 m/s^2),
d is the distance traveled.
4. Solve for distance traveled:
Rearrange the equation to solve for d:
d = W / (m * g * sin(0.06))
Calculate the distance (d) traveled using the power developed by the man (200 W), the combined mass of the man and the bicycle (80 kg), the acceleration due to gravity (9.8 m/s^2), and the angle of the grade (0.06).
5. Calculate speed:
Finally, divide the distance traveled (d) by the time it takes to cover that distance to find the speed (v).