Question

A cyclist intends to cycle up a 9.70¹⁰ hill whose vertical height is 145 m. The pedals tum in a circle If each complete revolution of the pedals moves the bike 4.80 m along its path, calculate the of diameter 36.0 cm average force that must be exerted on the pedals tangent to their circular path Neglect work done by friction and other losses. Express your answer to three significant figures and include the appropriate units.

Answer 1

To calculate the average force exerted on the pedals, divide the vertical height of the hill by the distance covered in one full revolution of the pedals. Then, calculate the circumference of the circular path covered by the pedals using the formula: Circumference = 2 × π × radius. Finally, divide the work done by the distance covered to find the average force exerted on the pedals.

Step-by-step explanation:

To calculate the average force exerted on the pedals, we first need to find the distance the cyclist needs to travel up the hill. We can do this by dividing the vertical height of the hill (145 m) by the distance covered in one full revolution of the pedals (4.80 m). This gives us:

Distance = vertical height / distance per revolution = 145 m / 4.80 m = 30.21 revolutions

Next, we can calculate the circumference of the circular path covered by the pedals using the formula:

Circumference = 2 × π × radius

Since the diameter of the circular path is given as 36.0 cm, the radius can be calculated as half of the diameter:

Radius = diameter / 2 = 36.0 cm / 2 = 18.0 cm = 0.18 m

Finally, we can calculate the average force exerted on the pedals by dividing the work done (product of force and distance) by the distance covered:

Average force = Work done / Distance = (145 m × 9.81 m/s²) / (30.21 revolutions × 4.80 m/revolution) = 47.94 N

Therefore, the average force that must be exerted on the pedals is 47.94 N.