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

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Answer 1 · 2017-05-28T06:20:57

The mass is $= 457.4 k g$ $=457.4kg$

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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,

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{4200}{9.8 (\frac{3}{5} \cdot cos (\frac{1}{8} π)) + sin (\frac{1}{8} π)}$ $=4200/(9.8(3/5*cos(1/8pi))+sin(1/8pi))$

$= 457.4 k g$ $=457.4kg$

A truck pulls boxes up an incline plane. The truck can exert a maximum force of 4,200N4,200 N. If the plane's incline is π8pi/8 and the coefficient of friction is 353/5 , what is the maximum mass that can be pulled up at one time?