Question

what force is required by a locomotive to pull/push 10 coaches each of mass 10^5 kg with to come at velocity of 100 m/s from rest? (ignore friction and aerodynamic force). find the work done by the locomotive if it displaced the coaches 1000 km

Answer 1

Correct question :

time is not given in your question . hence, i will take the time here as 100 s

                                                                                                                                   

To find :

• the force required by locomotive to push/pull 10 coaches
• the work done by locomotive

                                                                                                                                     

Given:

• mass of each coach, m = 10^5 kg
• initial velocity, u = 0 m/s
• final velocity, v = 100 m/s
• displacement , s= 1000 km

                                                                                                                                     

Formula to be used :

• acceleration = (v-u)/t
• force = mass*acceleration
• work = force * displacement

                                                                                                                                   

Solution :

we are given mass of 1 coach only , hence we need to find mass of 10 coach :

mass of 1 coach = 10^5 kg

$\implies \bold{mass\: of \:10\: coaches = 10*10^{5} }\\\\\implies \boxed{\bold{mass\:of\:10\:coaches = 10^6 kg}}$

                                                                                                                                   

we need to find acceleration to find the force:

acceleration = (v-u)/t

$\implies \bold{acceleration = \frac{100-0}{100} }\\\\\implies \bold{acceleration = \frac{100}{100}}\\\\\implies\boxed{\bold{acceleration = 1 m/s^2}}$

                                                                                                                                   

we have acceleration and mass , hence :

Force = acceleration * mass

$\implies\bold{force = 1 * 10^6}\\\implies\boxed{\bold{force = 10^6 N}}$

hence, required force = 10^6 N .

                                                                                                                                 

Displacement  = 1000 km

$\implies\bold{displacement = 1000*1000 m}\\\implies \bold{displacement = 10^6 m}$

work done  = force * displacement

$\implies \bold{work = force*displacement }\\\implies \bold{work = 10^6 * 10^6 }\\\implies\boxed{\bold{work = 10^{12} J}}$

                                                                                                                                         

hence,

$\implies\boxed{\bold{force = 10^6 N}}\\\implies\boxed{\bold{work = 10^{12} J}}$