A truck pulls boxes up an incline plane. The truck can exert a maximum force of $4, 000 N$ $4,000 N$ . If the plane's incline is $\frac{π}{3}$ $pi/3$ and the coefficient of friction is $\frac{1}{3}$ $1/3$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-07-25T12:52:05

The mass is $= 395.2 k g$ $=395.2kg$

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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,

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{4000}{9.8 (\frac{1}{3} \cdot cos (\frac{1}{3} π) + sin (\frac{1}{3} π))}$ $=4000/(9.8(1/3*cos(1/3pi)+sin(1/3pi))$

$= 395.2 k g$ $=395.2kg$

A truck pulls boxes up an incline plane. The truck can exert a maximum force of 4,000 N4,000N4,000 N. If the plane's incline is pi/3 π3pi/3 and the coefficient of friction is 1/3 131/3 , what is the maximum mass that can be pulled up at one time?