By Meghan Eisold
Many students at Colgate own Nalgene water bottles. I have been told that they are indestructible and that one would not even break if a car were to run over it. I decided to use physics to determine if this statement is true. To begin, I calculated the cross-sectional area of the water bottle and the force that the car would exert on it. I used these to determine the stress on the water bottle.
A=cross-sectional area of Nalgene
L=20 cm (0.20 m)
W=9 cm (0.09 m)
A = L x W (contact area)
A= 0.018 m2
Force of average-sized car=ma
F= 14,700 N
Stress= 14,700 N/0.018 m2
Stress= 816, 666 N/m2 = 816,666 Pa (0.8166 MPa)
Nalgene bottles are made of a material called Lenax (polycarbonate), which has a compressive strength of 12,500 psi. To put this in perspective, the compressive strength of a hard brick is about 12,000 psi. I compared this compressive strength to the magnitude of stress on the water bottle to determine if the bottle could withstand the force of the car.
Compressive strength of Lexan: 12,500 psi.
1 Psi = 6 894.75729 Pascals
12,500 Psi x (6894.757 Pa)/(1 Psi) = 861, 844, 662. 5 Pa
Compressive strength of Lexan = 861.4 MPa
861.4 MPa > 0.8166 MPa
Based on these calculations, the stress exerted on the Nalgene bottle by an average sized car is much smaller than the compressive strength of Lexan (the material from which Nalgene bottles are made). This means that the Nalgene bottle would not break under the force of an average sized vehicle. The actual results may vary somewhat due to the arched shape of the Nalgene bottle.