A truck of mass m_1 = 2000 kg is connected to a trailer of m_2 = 500 kg with a l

Question

A truck of mass m_1 = 2000 kg is connected to a trailer of m_2 = 500 kg with a light tow-bar as shown in the diagram. The is accelerating at a = 2 m s^-2 when its engine is providing a constant forward force P. The magnitudes of the total resistive forces opposing the motion of the truck and the trailer are F_1 = 1500 N and F_2 = 300 respectively. Draw separate free-body diagrams for both the truck and the trailer. Label clearly all the force arrows in your free-body diagrams. Calculate the magnitude of the tension T in the tow-bar. Calculate the magnitude of P. If the tow-bar suddenly breaks, describe the subsequent motions of the truck and the trailer, quoting the appropriate Newton's law(s). Assume the resistive forces F_1 and F_2 remain the same.

Explanation / Answer

Here, P   - F1 - F2 =   (M1 + M2)a

=>   P - 1500 - 300 = (2000 + 500) * 2

=> P = 6800 N

Also,   M1a = P - F1 - Tcos25

=>     2000 * 2 = 6800 - 1500 - Tcos25

=>   Tension, T =   1434.39 N

If Towbar breaks

=> acceleration of truck = (6800 - 1500)/2000

                                        = 2.65 m/sec2

=>   acceleration of trailer = (500 * 2 - 300)/500

                                         = 1.4 m/sec2

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