Power = (Rate of increase of potential energy)
A 6% grade is an angle of arctan 0.06 = 3.4336 degrees. The sine of that angle is 0.0599
200 = M*g*V sin3.4336
= 784 *V*0.0599
V = 4.25 m/s
A 6% grade is an angle of arctan 0.06 = 3.4336 degrees. The sine of that angle is 0.0599
200 = M*g*V sin3.4336
= 784 *V*0.0599
V = 4.25 m/s
Power = force * velocity
where power is given as 200 W.
First, let's calculate the force exerted by the man against gravity while riding up the 6 percent grade. The gradient of 6 percent indicates that for every 100 meters of horizontal distance, the elevation increases by 6 meters.
The force against gravity can be calculated using the formula:
Force = mass * gravity * grade
where:
- mass is the combined mass of the man and bicycle (80 kg),
- gravity is the acceleration due to gravity (approximately 9.8 m/s^2),
- grade is the percentage expressed as a decimal (6% = 0.06).
Substituting the values into the equation, we get:
Force = 80 kg * 9.8 m/s^2 * 0.06 = 47.04 N
Now, we can rearrange the power equation to solve for velocity:
Power = force * velocity
200 W = 47.04 N * velocity
Dividing both sides of the equation by 47.04 N, we get:
velocity = 200 W / 47.04 N
Calculating the result:
velocity ≈ 4.25 m/s
Therefore, the speed of riding up the 6 percent grade at a constant speed is approximately 4.25 m/s.