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Laws Of Motion

Question
CBSEENPH11016619

Discuss the horse cart problem on level road.

Solution

Let the cart be connected to horse through a string, as shown in the figure.
      
Let space T with italic rightwards arrow on top be the tension in the string.
For the cart to move, the horse presses the ground and the horse gets equal and opposite reaction space straight R with rightwards arrow on top.
Let F with rightwards arrow on top be the force of friction between cart and ground, and
Acceleration of system = straight a with rightwards arrow on top.
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From the free body diagram of horse given above
                            V = mg 
and                 H - T = ma                       ...(1) 
From the free body diagram of the cart, 
                    T - F = Ma                          ...(2)
Adding (1) and (2), we have,
                   H - F = (m+M)a
rightwards double arrow                     a equals fraction numerator H minus F over denominator m plus M end fraction
The system will move if and only if a>0.
i.e.                      H>F, for the cart to move.