(Hooke\'s Law) in Haiti, public transportation is often by taptaps, small pickup

Question

(Hooke's Law) in Haiti, public transportation is often by taptaps, small pickup trucks with seats along the sides of the pickup bed and railings to which passengers can hang on. Typically they carry two dozen or more passengers plus an assortment of chickens, goats, luggage, etc. Putting this much into the back of a pickup truck puts quite a large load on the truck springs. A truck has springs for each wheel, but for simplicity assume that the individual springs can be treated as one spring with a spring constant that includes the effect of all the springs. Also for simplicity, assume that all four springs compress equally when weight is added to the truck and that the equilibrium length of the springs is the length they have when they support the load of an empty truck. A 70 kg driver gets into an empty taptap to start the day's work. The springs compress 2.4 times 10^-2m. What is the effective spring constant of the spring system in the taptap?

Explanation / Answer

Hooke's Law states that the extension/compression of a spring is directly proportional to the force that stretches or compresses it.

So: F = - ks
Where F = Force
k = Spring constant
s = extension/compression

You have the mass of the driver, so we can find the force he exerts using Newton's Second Law ie F = mg

g = 9.81 m/s

So F = (70)(9.81) = 686.7 N

Back to Hooke's Law: F = -ks rearrange to give you k = F/s
k = 686.7/(2.4 x10^-2)
k = 28612.5 N/m

ignore the minus sign, that just indicates that the force is exerted in the opposite direction.

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