# Calculating Deceleration of Man on Bicycle with Air Resistance

• furor celtica
In summary, a man on a bicycle with a total mass of 100 kg is traveling at a constant speed of 15ms^-1 down a hill with a gradient of 10%. To slow down, he applies a constant braking force of 84 N. The air resistance is proportional to the square of the speed, and the deceleration when he first applies the brake is unknown. To solve this problem, we need to know the constant k in the air resistance equation, but it is not given. However, since there is no resultant force on the man and bicycle when he is freewheeling, we can determine that the air resistance is balanced by the component of the weight down the slope.
furor celtica

## Homework Statement

A man on a bicycle, of total mass 100 kg, is free-wheeling at a constant speed of 15ms^-1 down a hill with a gradient 10% (i.e. sin^-1(0.10)). He wants to slow down to a safer speed, so he applies the brake lightly to produce a constant braking force of 84 N. The air resistance is proportional to the square of the speed.
a. Calculate the deceleration when he first applies the brake.

## The Attempt at a Solution

Several other questions follow.
Anyway the problem is the air resistance: in this model I know v^2 but I don’t know the constant k as in kv^2! I know how to solve these problems with k but without it I’m lost. Is there a way to work around the air resistance, i.e. without using k?

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As he is freewheeling at constant speed initially, we know that there is no resultant force on him. (No acceleration) This means that the air resistance must be exactly balanced by the component of the weight (man + cycle) down the slope.

## What factors affect the deceleration of a person on a bicycle with air resistance?

The deceleration of a person on a bicycle with air resistance is affected by several factors, including the cyclist's speed, the surface area and shape of the cyclist and bicycle, the air density, and the coefficient of drag.

## How is deceleration due to air resistance calculated?

The deceleration due to air resistance can be calculated using the equation a = (1/2) * p * v^2 * c * A, where a is the deceleration, p is the air density, v is the cyclist's velocity, c is the coefficient of drag, and A is the surface area of the cyclist and bicycle.

## How does the cyclist's position on the bicycle affect deceleration?

The cyclist's position on the bicycle can impact the deceleration due to air resistance. For example, a more aerodynamic position, such as a tucked position, can reduce the surface area and decrease the coefficient of drag, resulting in less deceleration.

## Does the weight of the cyclist affect deceleration?

Yes, the weight of the cyclist can affect deceleration. A heavier cyclist may experience slightly more deceleration than a lighter cyclist due to the increased force of gravity pulling them down.

## How can deceleration due to air resistance be minimized?

Deceleration due to air resistance can be minimized by reducing the cyclist's speed, using a more aerodynamic position, and decreasing the surface area and coefficient of drag through equipment and clothing choices. Additionally, cycling in areas with lower air density can also decrease deceleration.

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