A truck pulls boxes up an incline plane. The truck can exert a maximum force of $2, 400 N$ $2,400 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{5}{3}$ $5/3$ , 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 $2, 400 N$ $2,400 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{5}{3}$ $5/3$ , what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2018-05-10T17:10:58

The truck will be able to pull up to 144 kg.

Explanation:

This calculation is neglecting any friction or gravity acting on the truck, so it's net force is 2400 N up the slope. Also, I'll take theta as $\frac{π}{3}$ $pi/3$ or 60˚. This is because $\frac{2 π}{3}$ $(2pi)/3$ is 120˚ and takes you beyond a vertical slope and back around to 60˚.

The parallel component of the gravitational force on the box is given by

$F_{g ∣ ∣} = m g sin (θ)$ $F_(g|\|)=mgsin(theta)$

This is the force that gravity exerts on the box down the slope.

The normal force acting on the box is given by the perpendicular component of the gravitational force

$N = m g cos (θ)$ $N=mgcos(theta)$

The frictional force is then given by

$F_{f} = μ_{s} N = μ_{s} m g cos (θ)$ $F_f=mu_sN=mu_smgcos(theta)$

$F_{g ∣ ∣}$ $F_(g|\|)$ and $F_{f}$ $F_f$ are the opposing forces so if we set the sum of these equal to 2400 N, that will allow us to solve for the maximum mass

$F_{g ∣ ∣} + F_{f} = 2400$ $F_(g|\|)+F_f=2400$

$\Rightarrow m g sin (θ) + μ_{s} m g cos (θ) = 2400$ $rArrmgsin(theta)+mu_smgcos(theta)=2400$

$\Rightarrow m (g sin (θ) + μ_{s} g cos (θ)) = 2400$ $rArrm(gsin(theta)+mu_sgcos(theta))=2400$

$\Rightarrow m = \frac{2400}{g sin (θ) + μ_{s} g cos (θ)}$ $rArrm=2400/(gsin(theta)+mu_sgcos(theta))$

$m = \frac{2400}{8.487 + 8.167} = 144 kg$ $m=2400/(8.487+8.167)=144" kg"$

Where

$g = 9.80 m/s$ $g=9.80" m/s"$

$μ_{s} = \frac{5}{3}$ $mu_s=5/3$

$θ = \frac{π}{3}$ $theta=pi/3$

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A truck pulls boxes up an incline plane. The truck can exert a maximum force of $2, 400 N$ $2,400 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{5}{3}$ $5/3$ , 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 2,400N2,400 N. If the plane's incline is 2π3(2 pi )/3 and the coefficient of friction is 535/3 , 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 $2, 400 N$ $2,400 N$ . If the plane's incline is $\frac{2 π}{3}$ $(2 pi )/3$ and the coefficient of friction is $\frac{5}{3}$ $5/3$ , what is the maximum mass that can be pulled up at one time?