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,""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:


"F-R_1-R_2=(m_1+m_2)a,""a=\\dfrac{F-R_1-R_2}{m_1+m_2},""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:


"F-R_1-T=m_1a,""T=F-R_1-m_1a,""T=2380\\ N-630\\ N-1400\\ kg\\cdot0.7\\ \\dfrac{m}{s^2}=770\\ N."

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