Answer to Question #157205 in Mechanics | Relativity for Ivo

Question #157205
A car is towing a carriage along a straight horizontal road by means of a tow-bar. The mass of the car is 1400kg and the mass of the carriage is 700kg. The non_gravitational resistances to the motion of the car and the cartiage are respectively 630N and 280N.
Given that when the car and the carriage are moving at 6m/s , the engine is working at 14.28KW, find
(a) the acceleration of the car
(b) the tension in the tow-bar
1
Expert's answer
2021-02-08T18:41:11-0500

(a) Let's first find the force that provides an engine of the car:


P=Fv,P=Fv,F=Pv=14.28103 W6 ms=2380 N.F=\dfrac{P}{v}=\dfrac{14.28\cdot10^3\ W}{6\ \dfrac{m}{s}}=2380\ N.

Then, we can find the acceleration of the car from the Newton's Second Law of Motion:


FR1R2=(m1+m2)a,F-R_1-R_2=(m_1+m_2)a,a=FR1R2m1+m2,a=\dfrac{F-R_1-R_2}{m_1+m_2},a=2380 N630 N280 N1400 kg+700 kg=0.7 ms2.a=\dfrac{2380\ N-630\ N-280\ N}{1400\ kg+700\ kg}=0.7\ \dfrac{m}{s^2}.

(b) Applying the Newton's Second Law of Motion, we get:


FR1T=m1a,F-R_1-T=m_1a,T=FR1m1a,T=F-R_1-m_1a,T=2380 N630 N1400 kg0.7 ms2=770 N.T=2380\ N-630\ N-1400\ kg\cdot0.7\ \dfrac{m}{s^2}=770\ N.

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