Learning Goal:
To understand the use of Hooke's law for a spring.
Hooke's law states that the restoring forceF⃗  on a spring when it has been stretched orcompressed is proportional to the displacementx⃗  of the spring from its equilibrium position.The equilibrium position is the position at which the spring isneither stretched nor compressed.
Recall that F⃗ âˆx⃗  means thatF⃗  is equal to a constant times x⃗ .For a spring, the proportionality constant is called the springconstant and denoted by k. The spring constant is aproperty of the spring and must be measured experimentally. Thelarger the value of k, the stiffer the spring.
In equation form, Hooke's law can be written
F⃗ =−kx⃗ .
The minus sign indicates that the force is in the oppositedirection to that of the spring's displacement from its equilibriumlength and is \"trying\" to restore the spring to itsequilibrium position. The magnitude of the force is given byF=kx, where x is the magnitudeof the displacement.
After driving a portion of the route, the taptap is fully loadedwith a total of 24 people including the driver, with an averagemass of 66 kg per person. In addition, there are three 15-kg goats,five 3-kgchickens, and a total of 25 kg of bananas on their way tothe market. Assume that the springs have somehow not yet compressedto their maximum amount. How much are the springs compressed?(Enter the compression numerically in meters using two significantfigures.)
