An object with a mass of $8 k g$ $8 kg$ is on a ramp at an incline of $\frac{π}{8}$ $pi/8$ . If the object is being pushed up the ramp with a force of $9 N$ $9 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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An object with a mass of $8 k g$ $8 kg$ is on a ramp at an incline of $\frac{π}{8}$ $pi/8$ . If the object is being pushed up the ramp with a force of $9 N$ $9 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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Answer 1 · 2017-07-21T03:55:40

$μ_{s} \geq 0.290$ $mu_s >= 0.290$

Explanation:

We're asked to find the minimum value of the coefficient of static friction $μ_{s}$ $mu_s$ between the incline and object so that the object remains stationary.

![d2gne97vdumgn3.cloudfront.net]( useruploads.socratic.org )

Since its mass is given as $8$ $8$ $kg$ $"kg"$ ,

$m g sin θ = (8 l kg) (9.81 l {m/s}^{2}) sin (\frac{π}{8}) = 30.0$ $mgsintheta = (8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)sin(pi/8) = 30.0$ $N$ $"N"$

The normal force magnitude $n$ $n$ is

$n = m g cos θ = (8 l kg) (9.81 l {m/s}^{2}) cos (\frac{π}{8}) = 72.5$ $n = mgcostheta = (8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)cos(pi/8) = 72.5$ $N$ $"N"$

Since the object is supposed to be stationary, the body is in equilibrium (sum of all forces acting on body equals zero), so (taking positive $x$ $x$ direction as up the incline)

$\sum F_{x} = F_{applied} + f_{s} - m g sin θ = 0$ $sumF_x = F_"applied" + f_s - mgsintheta = 0$

So

$f_{s} = m g sin θ - F_{applied}$ $f_s = mgsintheta - F_"applied"$

The applied force is given as $9$ $9$ $N$ $"N"$ , so we have

$f_{s} = 30.0$ $f_s = 30.0$ $N$ $"N"$ $- 9$ $- 9$ $N$ $"N"$ = $21.0$ $21.0$ $N$ $"N"$

Now that we know the static friction force $f_{s}$ $f_s$ , we can figure out the coefficient of static friction using the equation

$f_{s} \leq μ_{s} n$ $f_s <= mu_sn$

$μ_{s} \geq \frac{f_{s}}{n} = \frac{21.0 l N}{72.5 l N} = 0.290$ $mu_s >= (f_s)/n = (21.0color(white)(l)"N")/(72.5color(white)(l)"N") = color(red)(0.290$

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An object with a mass of $8 k g$ $8 kg$ is on a ramp at an incline of $\frac{π}{8}$ $pi/8$ . If the object is being pushed up the ramp with a force of $9 N$ $9 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer

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An object with a mass of 8kg 8 kg is on a ramp at an incline of π8pi/8 . If the object is being pushed up the ramp with a force of 9N 9 N, what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer

Explanation:

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An object with a mass of $8 k g$ $8 kg$ is on a ramp at an incline of $\frac{π}{8}$ $pi/8$ . If the object is being pushed up the ramp with a force of $9 N$ $9 N$ , what is the minimum coefficient of static friction needed for the object to remain put?