It is 5.0 km from your home to the Physics lab and your car is out of gas. You could run that distance
at 10 km/h, which uses up energy at the rate of 700 W; or you could walk it leisurely at 3.0 km/h,
which uses energy at 300 W.
(a) Calculate how much energy both choices would burn up.
(b) The conversion between energy units is: 1 Cal (food calaorie) = 1 kcal (kilocalorie) = 1000 cal
(thermochemical calorie) = 4184 J (joules). Calculate how much energy both choices would burn
up in units of J, cal and Cal.
(c) Which choice would burn up more energy?
a) E = Pt
for example the first way uses
700*1800 (30 minutes is 1800 seconds)
To answer these questions, we will first calculate the amount of energy burned up for both choices. Then we will convert the energy units to J (joules), cal (calories), and Cal (food calories). Finally, we will compare the energy burned for both choices to determine which one requires more energy.
(a) To calculate the energy burned up for each choice, we will use the formula:
Energy (Joules) = Power (Watts) × Time (seconds)
For running at 10 km/h, which uses up energy at the rate of 700 W:
Time = Distance / Speed
Time = 5.0 km / 10 km/h = 0.5 hours = 0.5 × 3600 seconds = 1800 seconds
Energy (Joules) = 700 W × 1800 s = 1,260,000 J
For walking leisurely at 3.0 km/h, which uses energy at 300 W:
Time = Distance / Speed
Time = 5.0 km / 3.0 km/h = 1.67 hours = 1.67 × 3600 seconds = 6000 seconds
Energy (Joules) = 300 W × 6000 s = 1,800,000 J
(b) To convert the energy values to cal (thermochemical calories), Cal (food calories), and kcal (kilocalories):
1 cal = 1/4184 J
1 Cal = 1 kcal = 1000 cal
For running at 10 km/h:
Energy (cal) = 1,260,000 J × (1 cal / 4184 J) = 301.68 cal
Energy (Cal) = 301.68 cal × (1 Cal / 1000 cal) = 0.30168 Cal
For walking leisurely at 3.0 km/h:
Energy (cal) = 1,800,000 J × (1 cal / 4184 J) = 430.00 cal
Energy (Cal) = 430.00 cal × (1 Cal / 1000 cal) = 0.43000 Cal
(c) To determine which choice burns up more energy, we compare the energy values calculated in part (b):
For running at 10 km/h: 0.30168 Cal
For walking leisurely at 3.0 km/h: 0.43000 Cal
Therefore, walking leisurely at 3.0 km/h would burn up more energy compared to running at 10 km/h.