Question

Consider a cart being pulled by a horse with constant velocity. The horse exerts force $\overrightarrow{F_{C,h}}$ on the cart. (The subscript indicate the force on the cart due to horse). The first subscript denotes the body on which force acts and second due to which it acts. (N = Normal reaction, ground is refering to surface which will apply normal force on contact and Earth is refering to gravitational pull on body by earth)

Choose the correct statement(s):

• A. ${\overrightarrow{f}}_{C,g},{\overrightarrow{N}}_{C,g},{\overrightarrow{N}}_{h,g}$ are external forces on a system consisting of horse and cart.
• B. ${\overrightarrow{F}}_{h,g}+{\overrightarrow{f}}_{C,g}=0$
• C. ${\overrightarrow{N}}_{C,g}$ and ${\overrightarrow{F}}_{C,E}$ are action reaction pairs
• D. ${\overrightarrow{F}}_{C,h}$ and ${\overrightarrow{f}}_{h,C}$ are action reaction pairs

Answer 1

Answer: (A), (B), (D)

The correct options are
A ${\overrightarrow{f}}_{C,g},{\overrightarrow{N}}_{C,g},{\overrightarrow{N}}_{h,g}$ are external forces on a system consisting of horse and cart.
B ${\overrightarrow{F}}_{h,g}+{\overrightarrow{f}}_{C,g}=0$
D ${\overrightarrow{F}}_{C,h}$ and ${\overrightarrow{f}}_{h,C}$ are action reaction pairs

Action reaction pair acts on different body and are in equal in magnitude and opposite in direction.Therefore, ${\overrightarrow{F}}_{C,h}$ and ${\overrightarrow{f}}_{h,C}$ are action reaction pairs but ${\overrightarrow{N}}_{C,g}$ and ${\overrightarrow{F}}_{C,E}$ are not action reaction pairs. Also, ${\overrightarrow{F}}_{h,g}+{\overrightarrow{f}}_{C,g}=0$.

For cart and horse system, all the forces which involve both cart and horshe term are internal (e.g-${\overrightarrow{F}}_{C,h}$) as they involve only those two bodies and all forces which involve another body except for these two will be external. Therefore, ${\overrightarrow{f}}_{C,g},{\overrightarrow{N}}_{C,g},{\overrightarrow{N}}_{h,g}$ are external forces on a system consisting of horse and cart.