Answer to Question #222693 in Classical Mechanics for Haddensen

Question

A car of mass 50tonnes pulls another car of mass 10tonnes, starting from rest the 2 masses attain a velocity of 20m/s in 5s. The coefficient of friction on each car equals 5N/tonne. Calculate

a) Force exerted by the engine

b) time required to cover 100m

 

Answer 1

$\text{Let}$

$m_1 = 50 t = 50000kg$

$m_2 = 10 t = 100000kg$

$v_0=0;v_1=20\frac{m}{s};t=5s$

$\mu = 5\frac{N}{t}= 0.005\frac{N}{kg}$

$F_{ex}-\text{Force exerted by the engine}$

$F_{fr}-\text{Friction force}$

$F = ma;F = F_{ex}-F_{fr}$

$a = \frac{v_1-v_0}{t}= \frac{20-0}{5}=4\frac{m}{s^2}$

$F_{fr}= \mu*m$

$m = m_1+m_2$

$a)$

$F_{ex}=F+F_{fr}= ma+\mu m=200250N$

$b)$

$S = v_0t +\frac{at^2}{2}$

$v_0 = 0$

$t =\sqrt{\frac{2S}{a}}=\sqrt{\frac{2*100}{4}}=7.07\frac{m}{s}$

$\text{Answer:}$

$a) F_{ex}=200250N$

$b)t =7.07\frac{m}{s}$