A truck pulls boxes up an incline plane. The truck can exert a maximum force of $2, 800 N$ $2,800 N$ . If the plane's incline is $\frac{3 π}{8}$ $(3 pi )/8$ and the coefficient of friction is $\frac{9}{7}$ $9/7$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-08-19T06:20:21

The mass is $417.7 k g$ $417.7kg$

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

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

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

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

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

Therefore,

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{2800}{9.8 (\frac{9}{7} \cdot cos (\frac{3}{8} π) + sin (\frac{3}{8} π))}$ $=2800/(9.8(9/7*cos(3/8pi)+sin(3/8pi))$

$= 417.7 k g$ $=417.7kg$

A truck pulls boxes up an incline plane. The truck can exert a maximum force of 2,800 N2,800N2,800 N. If the plane's incline is (3 pi )/8 3π8(3 pi )/8 and the coefficient of friction is 9/7 979/7 , what is the maximum mass that can be pulled up at one time?