A horse pulls an 8-ton wagon along a road where $\rho=\frac{1}{20}, e=\frac{1}{50}$. Starting from rest, it accelerates to a maximum speed of $v=2.4 \frac{\text{m}}{\sec }$ in 1 minute at $50 \mathrm{mp}$, while covering a distance of $120 \mathrm{~m}$. What is the power of this horse in horsepower? If it pulled uniformly throughout the journey, what is the traction force?[^0]


[^0]:    ${ }^{1}$ In this problem, $\rho$ is the coefficient of friction, and $e$ is the sine of the angle of inclination.
$1 \mathrm{p} 50 \mathrm{mp}-$ work $L=\frac{1}{2} m v^{2}+s \cdot p \cdot \sin \alpha+p \cdot s \cdot p \cdot \cos \alpha$. If we want the result in meter-kilograms, then in the second and third terms the force should be expressed in kilograms-force, the distance in meters, in the first term $\left(\frac{1}{2} m v^{2}\right)$, the mass in kilograms, the velocity in $\frac{\mathrm{m}}{\mathrm{sec}}$, and the whole expression should be divided by $g=9.81 \frac{\mathrm{m}}{\mathrm{sec}^{2}}$. The calculation shows that, at the precision level allowed by the nature of the problem, $\cos \alpha=1$ can be assumed.

$$
L=\left(\frac{800 \cdot 2.4^{2}}{2 \cdot 9.81}+120 \cdot 800 \cdot \frac{1}{50}+\frac{1}{20} \cdot 120 \cdot 800\right) \mathrm{mkg}=6955 \mathrm{mkg}
$$

Power $H=\frac{L}{110 \cdot 75}$ horsepower $=0.84$ horsepower.

$$
\text { Traction force }=\frac{L}{s} \mathrm{~kg} \text { weight }=58 \mathrm{~kg} \text { weight. }
$$

(László Bánó, Budapest.)

The problem was also solved by: I. Csada, P. Ehrenstein, R. Földes, A. Frank, V. Gráf, H. Grünhut, I. Koritsánszky, T. Pözel, O. Schwarz.