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 $\frac{5 π}{8}$ $(5 pi )/8$ and the coefficient of friction is $\frac{9}{8}$ $9/8$ , what is the maximum mass that can be pulled up at one time?

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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 $\frac{5 π}{8}$ $(5 pi )/8$ and the coefficient of friction is $\frac{9}{8}$ $9/8$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2018-03-08T06:26:31

The mass is $= 501.9 k g$ $=501.9kg$

Explanation:

![http://spmphysics.onlinetuition.com.my/2013/06/http://inclined-plane.html](https://useruploads.socratic.org/3SLPG4SgRIu153RhGHJq_inclined%20plane.jpg)

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

Let the force exerted by the truck be $F = 4000 N$ $F=4000N$

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

The coefficient of friction $μ = \frac{F_{r}}{N} = \frac{9}{8}$ $mu=F_r/N=9/8$

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

The angle of the plane is $θ = \frac{5}{8} π$ $theta=5/8pi$

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

Therefore,

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{4000}{9.8 (\frac{9}{8} \cdot cos (\frac{5}{8} π) + sin (\frac{5}{8} π))}$ $=4000/(9.8(9/8*cos(5/8pi)+sin(5/8pi))$

$= - 501.9 k g$ $=-501.9kg$

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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 $\frac{5 π}{8}$ $(5 pi )/8$ and the coefficient of friction is $\frac{9}{8}$ $9/8$ , what is the maximum mass that can be pulled up at one time?

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Explanation:

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A truck pulls boxes up an incline plane. The truck can exert a maximum force of 4,000N4,000 N. If the plane's incline is 5π8(5 pi )/8 and the coefficient of friction is 989/8 , what is the maximum mass that can be pulled up at one time?

1 Answer

Explanation:

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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 $\frac{5 π}{8}$ $(5 pi )/8$ and the coefficient of friction is $\frac{9}{8}$ $9/8$ , what is the maximum mass that can be pulled up at one time?