A truck pulls boxes up an incline plane. The truck can exert a maximum force of $4, 500 N$ $4,500 N$ . If the plane's incline is $\frac{π}{8}$ $pi/8$ and the coefficient of friction is $\frac{4}{3}$ $4/3$ , 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 $4, 500 N$ $4,500 N$ . If the plane's incline is $\frac{π}{8}$ $pi/8$ and the coefficient of friction is $\frac{4}{3}$ $4/3$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2018-01-15T15:42:42

The mass is $= 284.4 k g$ $=284.4kg$

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 $F = 4500 N$ $F=4500N$

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

The coefficient of friction $μ = \frac{F_{r}}{N} = \frac{4}{3}$ $mu=F_r/N=4/3$

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

The angle of the plane is $θ = \frac{1}{8} π$ $theta=1/8pi$

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

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

$= μ N + m g sin θ$ $=muN+mgsintheta$

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

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

$= \frac{4500}{9.8 (\frac{4}{3} \cdot cos (\frac{1}{8} π) + sin (\frac{1}{8} π))}$ $=4500/(9.8(4/3*cos(1/8pi)+sin(1/8pi))$

$= 284.4 k g$ $=284.4kg$

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A truck pulls boxes up an incline plane. The truck can exert a maximum force of $4, 500 N$ $4,500 N$ . If the plane's incline is $\frac{π}{8}$ $pi/8$ and the coefficient of friction is $\frac{4}{3}$ $4/3$ , 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 4,500 N4,500N4,500 N. If the plane's incline is pi/8 π8pi/8 and the coefficient of friction is 4/3 434/3 , 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 $4, 500 N$ $4,500 N$ . If the plane's incline is $\frac{π}{8}$ $pi/8$ and the coefficient of friction is $\frac{4}{3}$ $4/3$ , what is the maximum mass that can be pulled up at one time?