Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 19 minutes.

Part A
Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m2 and the density of air is 1.2 kg/m3.

Part B
What is this force as a fraction of the runner's weight?

Well, running on a treadmill definitely has its perks. No wind resistance means you won't have to battle against nature itself, just your own determination.

Part A - Drag Force Calculation:
To determine the drag force, we can use the following formula:

Drag Force = 0.5 * (Density of air) * (Velocity^2) * (Cross-Sectional Area) * (Drag Coefficient)

However, since the problem doesn't provide the velocity or the drag coefficient of the runner, we can't calculate the exact drag force. So let's move on to Part B and see if we can still bring some humor into this.

Part B - Drag Force as a Fraction of the Runner's Weight:
Now, converting everything into fractions can make things a bit complex, so let's simplify it a bit. Imagine the drag force is like a group of clowns trying to pull you down while you're running.

If we quantify the runner's weight as 1 (since it's a fraction of itself), and the drag force as D (also a fraction), we can write an equation like this:

D / 1 = ??? / 1

Since we don't have the exact values for the drag force or the runner's weight, we can't calculate the fraction. But let me tell you this, no matter how strong the drag force is, you are still the main attraction, the star of the show! So keep running, and don't let those pesky clowns get in your way!

Remember, a good sense of humor is key for overcoming any challenge, both on the track and off. Keep smiling and stay positive, my friend!

To determine the drag force experienced by the runner during the race, we can use the drag force equation:

Drag Force = (1/2) * (density of air) * (velocity^2) * (drag coefficient) * (cross-sectional area)

Given:
Runner's mass (m) = 60 kg
Distance (d) = 5.0 km = 5000 meters
Time (t) = 19 minutes = 19 * 60 = 1140 seconds
Cross-sectional area (A) = 0.72 m^2
Density of air (ρ) = 1.2 kg/m^3

First, let's determine the runner's average velocity during the race. We can use the equation:

Velocity (v) = Distance / Time

v = 5000 m / 1140 s
v ≈ 4.386 m/s

Now, let's calculate the drag force (F) using the formula mentioned earlier:

F = (1/2) * ρ * v^2 * (drag coefficient) * A

The drag coefficient depends on the shape and orientation of the runner. For simplicity, let's assume a typical value of 0.5 for a runner.

F = (1/2) * 1.2 kg/m^3 * (4.386 m/s)^2 * 0.5 * 0.72 m^2
F ≈ 1.414 N

Therefore, the drag force experienced by the runner during the race is approximately 1.414 Newtons.

Moving on to Part B, we need to determine the fraction of the runner's weight which is equal to the drag force:

Fraction = Drag Force / Weight

The weight of the runner can be calculated using the formula:

Weight = mass * acceleration due to gravity

Weight = 60 kg * 9.8 m/s^2
Weight ≈ 588 N

Fraction = 1.414 N / 588 N
Fraction ≈ 0.0024

Hence, the drag force experienced by the runner is approximately 0.0024 times the runner's weight.

11.2

A: 4.16 N

B: 4.16/588