The power developed by a man in riding up a 6 percent grade at a constant speed is 200 w. The man and his bicycle have a combined mass of 80 kg. Determine the speed of riding
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 pelt on wheel attains its operating speed of 800rev/min within 2 s after it is turned on. determine the constant angular acceleration of the pelton wheel. also find the total number of revolution the wheel makes before it attains its operating speed.
To determine the speed of riding, you can use the equation:
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.