Question #222693

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

 


1
Expert's answer
2021-08-04T04:40:30-0400

Let\text{Let}

m1=50t=50000kgm_1 = 50 t = 50000kg

m2=10t=100000kgm_2 = 10 t = 100000kg

v0=0;v1=20ms;t=5sv_0=0;v_1=20\frac{m}{s};t=5s

μ=5Nt=0.005Nkg\mu = 5\frac{N}{t}= 0.005\frac{N}{kg}

FexForce exerted by the engineF_{ex}-\text{Force exerted by the engine}

FfrFriction forceF_{fr}-\text{Friction force}

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

a=v1v0t=2005=4ms2a = \frac{v_1-v_0}{t}= \frac{20-0}{5}=4\frac{m}{s^2}

Ffr=μmF_{fr}= \mu*m

m=m1+m2m = m_1+m_2

a)a)

Fex=F+Ffr=ma+μm=200250NF_{ex}=F+F_{fr}= ma+\mu m=200250N

b)b)

S=v0t+at22S = v_0t +\frac{at^2}{2}

v0=0v_0 = 0

t=2Sa=21004=7.07mst =\sqrt{\frac{2S}{a}}=\sqrt{\frac{2*100}{4}}=7.07\frac{m}{s}


Answer:\text{Answer:}

a)Fex=200250Na) F_{ex}=200250N

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


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