Question

Noah is loading the ark and the last animal on board is a stubborn 1500-kg elephant who refuses to budge. Noah and his family pull the elephant at a constant speed up the 10° incline with a force of 10,000 N. What is the coefficient of sliding friction between the elephant and the loading platform?

Answer 1

The coefficient of sliding friction is 0.514

Explanation:

We start by writing the equations of motion of the elephant along the two directions, parallel and perpendicular, to the incline.

Along the parallel direction we have:

$F- mg sin \theta - \mu_k R = ma$ (1)

where :

F = 10,000 N is the force applied by Noah

$mg sin \theta$ is the component of the weight parallel to the incline, where:

m is the mass

g = 9.8 m/s^2 the acceleration of gravity

$\theta=10^{\circ}$  is the angle of incline

$\mu_k R$ is the force of friction, where:

$\mu_k$ is the coefficient of friction

R is the normal reaction  

and a is the acceleration

Perpendicular direction:

$R-mg cos \theta =0$ (2)

where $mg cos \theta$ is the component of the weight perpendicular to the incline

From (2) we find

$R=mg cos \theta$

And substituting into (1)

$F-mg sin \theta - \mu_k mg cos \theta = ma$

We know that the elephant moves at constant speed, so the acceleration is zero:

a = 0

So the equation becomes

$F-mg sin \theta - \mu_k mg cos \theta=0$

And we can re-arrange it to find the coefficient of friction:

$F-mg sin \theta - \mu_k mg cos \theta=0\\\mu_k = \frac{F-m g sin \theta}{mg cos \theta}=\frac{10000-(1500)(9.8)(sin 10)}{(1500)(9.8)(cos 10)}=0.514$

Learn more about friction and inclined planes:

brainly.com/question/5884009

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