Question

On your bike, you start from rest and accelerate to the speed of 5 m/s in 20 s (assume constant acceleration), and keep going at this speed on a level ground for further 500 m. During your trip, the average air drag force on you is 13 N, and the rolling friction force is 9 N. Assume 75 kg total mass of yourself and the bike, 20% mechanical energy efficiency in your body, and a BMR of 100 W. How much Calories you have spent to accomplish this?

Draw the energy model of the situation!
Hint: "Average air drag force" means that you can use the same value of the air drag over the whole travle distance, for both acceleration stage and motion with a constant speed. We know that the air drag force in fact depends on speed, but since the average value i you do not need to care about it.

Answer 1

The Calories spent during the bike ride can be calculated by finding the total work done against frictional forces, adjusting for mechanical energy efficiency, adding the BMR energy, and converting to Calories.

Step-by-step explanation:

To calculate the Calories spent during the bike ride, we consider two stages of the journey: acceleration and constant speed. First, we need to find the total work done against the air drag force and the rolling friction force. Then we convert that work into Calories, accounting for mechanical energy efficiency and the Basal Metabolic Rate (BMR).

The total distance during acceleration can be found using the equation d = (1/2) * a * t2, where a is the acceleration and t is the time. The acceleration a can be calculated using the equation a = (v - u) / t, where v is the final velocity, u is the initial velocity (zero in this case), and t is the time.

Once we have the total distance covered during acceleration, we can find the work done against the drag force and rolling friction for the acceleration part and add it to the work done during the constant speed phase. The total mechanical work (W) is given by W = Fd, where F is the total resistance force (sum of air drag and rolling friction) and d is the distance traveled.

To find out the Calories burned, we calculate the total energy output needed and divide by the mechanical energy efficiency:
E = W / efficiency, where E is the total energy output. Then, we add the BMR multiplied by the total time to account for the metabolic energy consumed during the trip. Finally, we convert the energy from Joules to Calories (1 Calorie = 4.184 kJ).