A truck pulls boxes up an incline plane. The truck can exert a maximum force of $3, 200 N$ $3,200 N$ . If the plane's incline is $\frac{π}{8}$ $pi/8$ and the coefficient of friction is $\frac{4}{5}$ $4/5$ , what is the maximum mass that can be pulled up at one time?

Question

1431 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-21T12:52:33

The maximum mass is $= 291.1 k g$ $=291.1kg$

enter image source here

Resolving in the direction parallel to the plane $↗^{+}$ $↗^+$

Let the force exerted by the truck be $F = 3200 N$ $F=3200N$

Let the frictional force be $= F_{r} N$ $=F_rN$

The coefficient of friction $μ = \frac{F_{r}}{N} = \frac{4}{5}$ $mu=F_r/N=4/5$

The normal force is $N = m g cos θ$ $N=mgcostheta$

The angle of the plane is $θ = \frac{π}{8}$ $theta=pi/8$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$
Therefore,

$F = F_{r} + m g sin θ$ $F=F_r+mgsintheta$

$= μ N + m g sin θ$ $=muN+mgsintheta$

$= μ m g cos θ + m g sin θ$ $=mumgcostheta+mgsintheta$

$m = \frac{F}{g (μ cos θ + sin θ)}$ $m=F/(g(mucostheta+sintheta))$

$= \frac{3200}{9.8 (\frac{4}{5} \cdot cos (\frac{1}{8} π) + sin (\frac{1}{8} π))}$ $=3200/(9.8(4/5*cos(1/8pi)+sin(1/8pi))$

$= 291.1 k g$ $=291.1kg$

A truck pulls boxes up an incline plane. The truck can exert a maximum force of 3,200N3,200 N. If the plane's incline is π8pi/8 and the coefficient of friction is 454/5 , what is the maximum mass that can be pulled up at one time?