Answer to Question #157205 in Mechanics | Relativity for Ivo

Question

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

Answer 1

(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:

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