Question

You tug on the leash of your stubborn dog which does not want to move such that for the dog, tension $\overrightarrow{T}$ acts at some angle $\theta$ above the horizontal, as shown in the diagram.
Which of the following statements is true about $\overrightarrow{T}$ in relation to the other forces? The other forces are implied (and also shown in the diagram).

• A. $\left|F_N\right|=\left|T\right|$
• B. $\left|F_N\right|=\left|mg\right|$
• C. $\left|F_N\right|=|mg-T|$
• D. $\left|F_N\right|>\left|mg\right|$
• E. $\left|F_N\right|<\left|mg\right|$

Answer 1

The correct option is E $\left|F_N\right|<\left|mg\right|$

Let the tension force makes an angle $\theta$ with the horizontal direction.

As the dog is in equilibrium, thus the net force on the dog is zero.

Horizontal direction : $Tcos\theta =f$

Vertical direction : $|F_N|+Tsin\theta =mg$

$\therefore$ $|F_N|=|mg-Tsin\theta |$ $⟹|F_N|<|mg|$