A 60kg bicyclist (including the bicycle) is pedaling to the
right, causing her speed to increase at a rate of 3.1 m/s2,
despite experiencing a 60N drag. Neglect any friction
impeding her motion.

How many forces are acting on the bicyclist?

What is the magnitude of the net force on the bicyclist?

How much force is the bicyclist generating through her
pedaling?

a) 4 forces

b) 186 N

c) 246 N

Explanation:

a)

Let's count the forces acting on the bicylist:

1) Weight (): this is the gravitational force exerted on the bicyclist by the Earth, which pulls the bicyclist towards the Earth's centre; so, this force acts downward (m = mass of the bicyclist, g = acceleration due to gravity)

2) Normal reaction (N): this is the reaction force exerted by the road on the bicyclist. This force acts vertically upward, and it balances the weight, so its magnitude is equal to the weight of the bicyclist, and its direction is opposite

3) Applied force (): this is the force exerted by the bicylicist to push the bike forward. Its direction is forward

4) Air drag (): this is the force exerted by the air on the bicyclist and resisting the motion of the bike; its direction is opposite to the motion of the bike, so it is in the backward direction

So, we have 4 forces in total.

b)

Here we can find the net force on the bicyclist by using Newton's second law of motion, which states that the net force acting on a body is equal to the product between the mass of the body and its acceleration:

where

is the net force

m is the mass of the body

a is its acceleration

In this problem we have:

m = 60 kg is the mass of the bicyclist

is its acceleration

Substituting, we find the net force on the bicyclist:

c)

We can write the net force acting on the bicyclist in the horizontal direction as the resultant of the two forces acting along this direction, so:

where:

is the net force

is the applied force (forward)

is the air drag (backward)

In this problem we have:

is the net force (found in part b)

is the magnitude of the air drag

Solving for , we find the force produced by the bicyclist while pedaling:

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