A truck pulls boxes up an incline plane. The truck can exert a maximum force of $3, 600 N$ $3,600 N$ . If the plane's incline is $\frac{3 π}{8}$ $(3 pi )/8$ and the coefficient of friction is $\frac{9}{4}$ $9/4$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-12-23T13:32:38

The mass is $= 205.8 k g$ $=205.8kg$

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

Let the force exerted by the truck be $F = 3600 N$ $F=3600N$

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

The coefficient of friction $μ = \frac{F_{r}}{N} = \frac{9}{4}$ $mu=F_r/N=9/4$

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

The angle of the plane is $θ = \frac{3}{8} π$ $theta=3/8pi$

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

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{3600}{9.8 (\frac{9}{4} \cdot cos (\frac{3}{8} π) + sin (\frac{3}{8} π))}$ $=3600/(9.8(9/4*cos(3/8pi)+sin(3/8pi))$

$= 205.8 k g$ $=205.8kg$

A truck pulls boxes up an incline plane. The truck can exert a maximum force of 3,600N3,600 N. If the plane's incline is 3π8(3 pi )/8 and the coefficient of friction is 949/4 , what is the maximum mass that can be pulled up at one time?