Question

A\[500kg\]horse pulls a cart of mass\[1500kg\]along a level road with an acceleration of\[1m{{s}^{-2}}\]. If the coefficient of sliding friction is\[0.2\], then the force exerted by the horse in forward direction is
        \[\begin{align}
  & A)4500N \\
 & B)4000N \\
 & C)5000N \\
 & D)6000N \\
\end{align}\]

Answer 1

Hint: Here if the horse needs to move the cart with the given acceleration, it will have to overcome the frictional force exerted by earth on the weight of the cart. This force will be given by the product of coefficient of sliding friction to the weight of the cart. Now if it needs to acquire the given acceleration it will need to exert more force. So the total force will be the sum of both force needed to overcome friction and force needed to gain the acceleration.
     Formula Used: \[{{F}_{friction}}=\mu \times {{M}_{total}}g\]
                                    \[F={{M}_{total}}a\]
    Complete Solution: Firstly we will look at the frictional force exerted by the earth on the masses. The coefficient of sliding friction is given by\[0.2\].

The combined mass of horse and cart is \[{{M}_{total}}={{m}_{horse}}+{{m}_{cart}}=500+1500=2000kg\]
Now, the frictional force due to sliding is given by, \[{{F}_{friction}}=\mu \times {{M}_{cart}}g\]
\[{{F}_{friction}}=0.2\times 1500\times 10=3000N\]
So, the force exerted by earth on the cart is 3000N.
Now, if we calculate the force needed for acquiring the acceleration of\[1m{{s}^{-2}}\]. It will be,
\[\begin{align}
  & F={{M}_{total}}a \\
 & F=2000\times 1=2000N \\
\end{align}\]
So, the force needed for acquiring\[1m{{s}^{-2}}\]is 2000N.
Now, if we need the total force exerted by horse will be,
\[{{F}_{horse}}={{F}_{friction}}+F=3000+2000=5000N\]

Therefore, the correct answer is option c.

Note: Here, there is a chance for creating mistakes because we will take only the mass of the cart and calculate the force for gaining the acceleration. But actually the horse itself will be having a mass and it will need to exert force for pulling its own weight. The sliding friction is only applicable for the cart because it is the only sliding body.