Question

Suppose a horse leans against a wall, as in Figure 9.31. Calculate the force exerted on the wall assuming that force is horizontal while using the data in the schematic representation of the situation. Note that the force exerted on the wall is equal in magnitude and opposite in direction to the force exerted on the horse, keeping it in equilibrium. The total mass of the horse and rider is . Take the data to be accurate to three digits.

Short answer

The force on the wall is$1429.17\mathrm{N}$

Step-by-step solution

Concept

The torque on a rotating object depends upon the force and theperpendicular distance from the force F to the point of the pivot.

Given Data

The total mass of the horse and the rider is, $m=500\mathrm{kg}$.

The perpendicular distance from the center of mass of the horse and rider to the toe of the horse is$r_1=0.35\mathrm{m}$.

The perpendicular distance from the toe of the horse to the force exerted by the wall is,$r=1.2\mathrm{m}$.

Step 3:Calculation of the force

The torque is,

$\tau =rmg$

Here g is the gravitational acceleration.

The torque at the toe due to the weight of the horse and rider is,

$$\begin{gathered} r_1=500\times 9.8\times 0.35 \\ =1715\mathrm{N}·\mathrm{m} \end{gathered}$$

The torque at the toe of the horse due to horizontal is,

$$\begin{gathered} {\tau }_2=r_2\times F_{wall} \\ {F}_{wall}=\frac{{\tau }_2}{r_2} \end{gathered}$$

Here$F_{wall}$ is the force on the wall.

Substitute the values in the above expression, and we get,

$\begin{array}{l}{F}_{wall}=\frac{1715}{1.2}\\ F_{wall}=1429.17\mathrm{N}\end{array}$

Thus, the force on the wall is $1429.1\mathrm{N}$.