If each complete revolution of the pedals moves the bike 5.00m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 38.4cm.
To calculate the average force exerted on the pedals tangent to their circular path, we need to use the formula for average force:
Average force = (mass * change in velocity) / time
In this case, we can assume that the mass of the bike and the rider remains constant, and we can neglect the time taken to complete a revolution of the pedals since it is not provided in the question. So, the average force can be simplified to:
Average force = mass * change in velocity
First, let's calculate the change in velocity. The distance moved along the path for each revolution of the pedals is given as 5.00m. Since the pedals turn in a circle of diameter 38.4cm, the circumference of the circular path can be calculated as:
Circumference = π * diameter
Substituting the given values:
Circumference = 3.14 * 38.4cm
Now, we need to convert the circumference to meters since the distance moved is given in meters:
Circumference = 3.14 * 0.384m
Next, we calculate the change in velocity:
Change in velocity = distance / time
Since a complete revolution of the pedals moves the bike 5.00m, and we need to find the time taken for one revolution, we can rearrange the formula:
Time = distance / change in velocity
Substituting the given values:
Time = 5.00m / (3.14 * 0.384m)
Now, we have the time taken for one revolution. However, we need to calculate the change in velocity, so let's reverse the formula:
Change in velocity = distance / time
Substituting the given values:
Change in velocity = 5.00m / (5.00m / (3.14 * 0.384m))
Simplifying the expression:
Change in velocity = 3.14 * 0.384m
Now that we have the change in velocity, we can calculate the average force by multiplying it by the mass:
Average force = mass * change in velocity
However, the mass of the bike and the rider is not provided in the question, so we are unable to calculate the exact average force without this information.