question_answer

A car of mass 'm' kg and a truck of mass ?10 m? kg are moving with the same velocity. The force required to stop the car in a certain distance is 'F' N. Then the force required to stop the truck through the same distance is ______.

Answer:

As both the car and the truck are coming to rest, their final velocity is 0. \[{{m}_{1}}=5\]quintals = 500 kg \[{{m}_{2}}=5\]tons = 5000 kg \[{{u}_{1}}={{u}_{2}}\] \[{{v}_{1}}={{v}_{2}}\] \[{{s}_{1}}={{s}_{2}}\] \[{{F}_{1}}=100N\] \[{{F}_{2}}=?\] \[F=ma\] .........(1) How to get ?a? from the given data S, u and v? The relation between v, u and S is \[{{v}^{2}}-{{u}^{2}}=2aS\] \[\Rightarrow {{0}^{2}}-{{u}^{2}}=2aS\Rightarrow a=-\frac{{{u}^{2}}}{2S}\] ???(2) Substituting (2) in (1), we get \[\Rightarrow F=-\frac{m{{u}^{2}}}{2S}\Rightarrow F\propto m\] [\[\because \] u and S are same] \[\frac{{{F}_{2}}}{{{F}_{1}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] \[\Rightarrow \frac{{{F}_{2}}}{100}=\frac{5000}{500}\] \[{{F}_{2}}=1000\,\,F\] Therefore a force required to stop a truck is 1000 times the force required to stop the car through the same distance.