Suppose a 65-kg person can run 1000m in 5min. Assume that each stride is 1.5m long, and with each stride the runner must supply an amount of energy equal to her kinetic energy. How much energy (in food calories) is required to run 1km? Is your answer realistic?
To find out how much energy is required to run 1 km, we need to calculate the kinetic energy of the runner and then convert it into food calories.
First, let's calculate the total distance covered by the runner in meters. Since each stride is 1.5m long, the runner takes 1000m / 1.5m = 667 strides.
Next, let's calculate the time taken for one stride. The runner completes the 1000m in 5 minutes. So, the time taken for one stride is 5 minutes / 667 strides = 0.0075 minutes (since there are 60 seconds in a minute).
Now, we can calculate the velocity of the runner. Since each stride is 1.5m long and the time taken for one stride is 0.0075 minutes, the velocity can be calculated as follows: Velocity = Distance / Time = 1.5m / (0.0075/60) minutes = 120 m/minute.
Next, let's calculate the kinetic energy of the runner using the formula: Kinetic Energy = 0.5 * mass * velocity^2.
Given that the mass of the runner is 65 kg and the velocity is 120 m/minute, the kinetic energy can be calculated as follows: Kinetic Energy = 0.5 * 65 kg * (120 m/minute)^2.
After calculating this expression, we find that the kinetic energy is equal to 468,000 kilogram-meter^2/minute^2.
To convert this energy into food calories, we need to multiply it by the conversion factor of 0.000239006 food calories per kilogram-meter^2/minute^2.
So, the energy required to run 1 km is 468,000 kilogram-meter^2/minute^2 * 0.000239006 food calories per kilogram-meter^2/minute^2 = 111.91 food calories.
Is this answer realistic?
Yes, this answer is realistic. Running can burn a significant amount of calories, and 111.91 food calories is a reasonable estimate for the energy required for a 65 kg person to run 1 km.
To calculate the energy required to run 1 km, we need to consider the kinetic energy associated with each stride made by the runner. The kinetic energy of an object can be calculated using the formula:
Kinetic Energy = (1/2) * mass * velocity^2.
Given that each stride is 1.5 m long and the runner can run 1000 m in 5 minutes, we can find their average velocity as follows:
Average Velocity = Distance / Time = 1000 m / 5 min = 200 m/min.
Now, let's convert the average velocity to meters per second (m/s):
Average Velocity = 200 m/min * (1 min / 60 s) = 3.33 m/s.
Since each stride is 1.5 m long, we can determine the number of strides per meter:
Number of Strides per Meter = 1 m / 1.5 m = 0.67 strides/m.
Now, to calculate the total number of strides required to run 1 km:
Number of Strides in 1 km = 1000 m * 0.67 strides/m = 670 strides.
Next, we can calculate the total energy required:
Total Energy = Number of Strides in 1 km * Kinetic Energy per Stride.
To find the kinetic energy per stride, we substitute the mass of the person, which is 65 kg, and the velocity per stride, which is the average velocity divided by the number of strides per meter:
Kinetic Energy per Stride = (1/2) * mass * (velocity per stride)^2.
Since each stride covers 1.5 m and we have the total distance of 1000 m, the velocity per stride is:
Velocity per Stride = (Average Velocity * time per stride)/(Stride Length)
= (3.33 m/s * 60s) / 1.5 m
= 13.32 m/s.
Now we can calculate the energy per stride:
Kinetic Energy per Stride = (1/2) * 65 kg * (13.32 m/s)^2.
Finally, we can calculate the total energy required to run 1 km:
Total Energy = Number of Strides in 1 km * Kinetic Energy per Stride.
Please note that the mass of the person and the distance they can run in a given time are provided in the question. However, if there were missing values or different variables, the calculations might be adjusted accordingly.
Now, let's calculate the result.