Question

4. (a) The springs of a pickup truck act like a single spring with a force constant of 1.30×105N/m. By how much will the truck be depressed by its maximum load of 1000 kg?
(b) If the pickup truck has four identical springs, what is the force constant of each?

Please include all of the steps.

Answer 1

• Force applied on load=mg=1000(9.8)=9800N
• Spring constant=k=1.30×10^5N/m

Now

$\\ \rm\rightarrowtail F=-kx[tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-F}{k}$

$\\ \rm\rightarrowtail x=\dfrac{-9800}{1.3\times 10^5}$

$\\ \rm\rightarrowtail x=-7538.5\times 10^{-5}m$

$\\ \rm\rightarrowtail x=-0.075385m$

#b

$\\ \rm\rightarrowtail F=-k\delta x$

$\\ \rm\rightarrowtail k\delta x=-F$

$\\ \rm\rightarrowtail k\delta x=-9800/4$

$\\ \rm\rightarrowtail k\delta x=-2450$

$\\ \rm\rightarrowtail k=-2450/-0.075385$

$\\ \rm\rightarrowtail k=3.25\times 10^4N/m$