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 determine the energy required to run 1 km, we can follow these steps:
Step 1: Find the total number of strides taken to cover 1 km.
Given that each stride is 1.5 m long, we can calculate the number of strides using the formula: Total distance / Length of each stride.
So, for 1 km:
Number of strides = (1 km) / (1.5 m/stride) = (1000 m) / (1.5 m/stride) = 666.67 strides (approximately)
Step 2: Calculate the total distance covered (in meters) in these strides.
Total distance covered = Number of strides * Length of each stride
Total distance covered = 666.67 strides * 1.5 m/stride = 1000 m
Step 3: Calculate the kinetic energy required to cover this distance.
The kinetic energy formula can be expressed as: KE = 0.5 * mass * velocity^2
Given that mass = 65 kg and velocity = distance / time, we can find the velocity as:
Velocity = Total distance covered / Total time taken
Velocity = 1000 m / 5 min = 200 m/min = (200 m/min) / (60 s/min) = 3.33 m/s
Substituting the values into the formula:
Kinetic energy = 0.5 * (65 kg) * (3.33 m/s)^2 = 363.08 Joules
Step 4: Convert the energy from joules to food calories.
1 calorie = 4.184 joules (approximately)
So, the energy required to run 1 km is:
363.08 J * (1 calorie / 4.184 J) = 86.83 calories
Is the answer realistic?
Yes, the answer is realistic. Running requires energy expenditure, and it is common for a person to burn calories while running. The calculated amount of energy, 86.83 calories, seems reasonable for a 65-kg person running 1 km.
To calculate the energy required to run 1km, we need to first determine the number of strides taken to cover that distance.
Given that each stride is 1.5m long, the total number of strides to cover 1km (1000m) would be:
Number of strides = Distance / Stride length
Number of strides = 1000m / 1.5m = 666.67 strides
Next, we need to determine the energy required to supply the kinetic energy for each stride. The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
Since the person's velocity is not provided, we can estimate it using the information provided in the question. The person runs 1000m in 5 minutes, so their average velocity can be calculated as:
Velocity = Distance / Time
Velocity = 1000m / 5min = 200m/min
To convert this to meters per second (m/s), we divide by 60 (minutes to seconds):
Velocity = 200m/min / 60s/min = 3.33 m/s (approximately)
Now we can calculate the kinetic energy for each stride:
Kinetic energy = 0.5 * mass * velocity^2
Plugging in the values:
Kinetic energy = 0.5 * 65kg * (3.33m/s)^2
Kinetic energy ≈ 362.75 Joules
To convert this energy value to food calories, we can use the conversion factor that 1 food calorie (Cal) is equal to approximately 4.184 Joules. So:
Energy in calories = Energy in joules / 4.184
Energy in calories ≈ 362.75 J / 4.184 Cal ≈ 86.77 calories
Therefore, approximately 86.77 food calories are required to run 1km under the given assumptions.
Now, regarding the realism of this answer, it is important to note that this is an estimation based on the given information and some assumptions. Actual energy expenditure during running can vary based on factors such as individual metabolism, efficiency of movement, running technique, and terrain. Additionally, energy expenditure can also be affected by factors like altitude and temperature. So, while this calculation provides a rough estimate, the actual energy required to run 1km can vary from person to person.