# A truck pulls boxes up an incline plane. The truck can exert a maximum force of 3,200 N. If the plane's incline is pi/8  and the coefficient of friction is 3/5 , what is the maximum mass that can be pulled up at one time?

May 23, 2016

$m \le 350.11 \text{ } k g$

#### Explanation:

$T \ge m \cdot g \cdot \sin \alpha + {u}_{k} \cdot m \cdot g \cos \alpha$

$T = 3200 N$

${U}_{k} = \frac{3}{5}$

$\alpha = \frac{\pi}{8}$

$T \ge m \left(g \cdot \sin \alpha + {u}_{k} \cdot g \cdot \cos \alpha\right)$

$m \le \frac{T}{g \cdot \sin \alpha + {u}_{k} \cdot g \cdot \cos \alpha}$

m<=3200/(g(sin alpha+u_k cos alpha)

$m \le \frac{3200}{g \left(0.38 + 0.6 \cdot 0.92\right)}$

$m \le \frac{3200}{9.14}$

$m \le 350.11 \text{ } k g$