To find the amount of energy needed to walk three flights of stairs, we can calculate the gravitational potential energy gained. By converting the weight from kilograms to newtons, determining the total height climbed, and using the formula PE = mgh, we find that it requires approximately 678 calories of energy.
To calculate the amount of energy needed to walk the three flights of stairs, we need to find the gravitational potential energy gained. The formula for gravitational potential energy is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
First, we need to convert the weight from kilograms to newtons using the formula W = mg. Since the mass is given in kilograms and the acceleration due to gravity is approximately 9.8 m/s^2, we have W = 48 kg * 9.8 m/s^2 = 470.4 N.
Next, we calculate the total height climbed by multiplying the height of one step by the number of steps. The height of one step is given as 6 inches, which is equivalent to 0.1524 meters. So the total height is 0.1524 m/step * 40 steps = 6.096 m.
Finally, we can calculate the gravitational potential energy using the formula PE = mgh. Thus, PE = 48 kg * 9.8 m/s^2 * 6.096 m = 2833.6312 J. Since 1 calorie is equal to 4.184 J, we can convert the energy to calories by dividing the value by 4.184. Therefore, the amount of energy needed to walk the three flights of stairs is 2833.6312 J / 4.184 J/cal = 677.8885 cal. Rounded to the nearest whole number, the answer is approximately 678 calories.