With one of the year’s most popular shopping days behind us, I decided to reflect on the physics of shopping to see exactly what physical toll those Black Friday deals take on our bodies.
To clearly paint this picture, let me narrate an example story. To prepare for the winter snowstorm making its way towards Colgate, you decide that you want to buy a new sweater, pants, winter coat, hat, pair of gloves, scarf, and high boots to help you bundle and keep warm.
You enter the store walking at an average human walking speed of 3 mph (1.34 m/s) when you see THE perfect winter sweater hanging on the rack and increase your speed to an average running speed of 2.62 m/s in just 3 seconds. This means that your acceleration is 0.43 m/s^2, requiring a change in kinetic energy equal to 195 J.
3 mi / 1 hr * 1609 m / 1 mi * 1 hr / 3600 s = 1.34 m/s
1 mi / 10.21 min * 1609 m / 1 mi * 1 min / 60 s = 2.62 m/s
a = (vf - vi) / t = (2.62 m/s - 1.34 m/s) / 3 seconds = 0.43 m/s^2
KEi = 0.5mv^2 = 0.5 * 77 kg * ((1.34 m/s)^2) = 69.1 J
KEf = 0.5mv^2 = 0.5 * 77 kg * ((2.62 m/s)^2) = 264.3 J
Change in KE = KEf - KEi = 264.3 J - 69.1 J = 195 J
Therefore, being an average American female weighing 77 kg and standing 1.65 m tall, you need to exert a force of 33.1 N in the x-direction to get that sweater before someone else does.
F = ma
F = 77 kg (0.43 m/s^2)
F = 33.1 N
The average masses for these items you purchased are as follows: 0.5 kg for a sweater, 0.4 kg for pants, 3 kg for a coat, 0.2 kg for a hat, 0.15 for gloves, 0.3 kg for a scarf, and 1.8 kg for boots. Although you are environmentally conscious, you forgot to bring your reusable shopping bag and had to collect your new items in a plastic shopping bag that has a mass of 0.0055 kg.
Based on these measurements, your new purchases achieved a total mass of 6.36 kg. Therefore, if you are holding this bag straight at the side of your thigh (ignore slight angle from how the bags project), it exerts a force of about 62.3 N downward.
m = 0.5 kg + 0.4 kg, 3 kg, 0.2 kg, 0.15 kg, 0.3 kg, 1.8 kg = 6.36 kg
F = ma = mg
F = 6.36 kg (9.8 m/s^2)
F = 62.3 N
Therefore, according to Newton’s First and Third Law of motion, your arm muscles need to exert 62.3 N of force in the upward direction to keep the bag at rest at your side.
Maybe Cyber Monday online shopping seems like a much better idea for your arm (not so much your bank account though)!
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