A truck pulls boxes up an incline plane. The truck can exert a maximum force of $5, 600 N$ $5,600 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{7}{6}$ $7/6$ , 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 $5, 600 N$ $5,600 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{7}{6}$ $7/6$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2016-05-01T09:02:55

979 kg

Explanation:

enter image source here

Note, by definition, an inclined plane cannot have an inclination more than $\frac{π}{2}$ $pi/2$ . I take the angle is measured from positive x-axis, so it is just $θ = \frac{π}{3}$ $theta = pi/3$ the other way.

here $f$ $f$ is the applied force, NOT the frictional force.

So, as we can easily observe in the picture, the forces that oppose will be (m is expressed in $k g$ $kg$ ):

gravitational pull: $m g sin θ = 9.8 \times \frac{\sqrt{3}}{2} m = 8.49 m N$ $mgsintheta = 9.8xxsqrt3/2 m=8.49mN$
frictional force, opposite to the direction of tendency of movement: $μ m g cos θ = \frac{7}{6} \times 9.8 \times \frac{1}{2} m N = 5.72 m N$ $mumgcostheta = 7/6xx9.8xx1/2 mN = 5.72m N$

Hence total is: $(8.49 + 5.72) m N = 14.21 m N$ $(8.49+5.72)m N=14.21m N$

So, for the truck the to be able to pull it up, the maximum force it can exert must be more than this:

$5600 N > 5.72 m N \Rightarrow m < 979 k g$ $5600N>5.72m N => m<979 kg$

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A truck pulls boxes up an incline plane. The truck can exert a maximum force of $5, 600 N$ $5,600 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{7}{6}$ $7/6$ , what is the maximum mass that can be pulled up at one time?

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1 Answer

Explanation:

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A truck pulls boxes up an incline plane. The truck can exert a maximum force of $5, 600 N$ $5,600 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{7}{6}$ $7/6$ , what is the maximum mass that can be pulled up at one time?