An object with a mass of $9$ $9$ $k g$ $kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $15$ $15$ $N$ $N$ to start pushing the object down the plane and $7$ $7$ $N$ $N$ to keep pushing it, what are the coefficients of static and kinetic friction?

Question

An object with a mass of $9$ $9$ $k g$ $kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $15$ $15$ $N$ $N$ to start pushing the object down the plane and $7$ $7$ $N$ $N$ to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

Impact of this question

1417 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-25T00:23:16

The coefficient of static friction is $μ_{s} = 1.24$ $mu_s=1.24$ and the coefficient of kinetic friction is $μ_{k} = 1.11$ $mu_k=1.11$ .

Explanation:

The negative sign on the angle is not relevant in this case: the angle of the inclined plane is $\frac{π}{4}$ $pi/4$ $r a d i a n s$ $radians$ ( $45^{o}$ $45^o$ ). The negative sign just shows that the slope increases right-to-left rather than left-to-right.

The force perpendicular to the plane, the normal force, will be given by:

$F_N=mgsinTheta=9*9.8*sin(pi/4)=62.4$ $N$

Based on this, the frictional force will be:

$F_"frict"=muF_N$

Rearranging,

$mu=(F_"frict")/(F_N)$

We will find two different values, the static friction, $mu_s$ , and the kinetic friction, $mu_k$ .

The force parallel to the plane due to gravity will be given by:

$F=mgcosTheta=9*9.8*cos(pi/4)=62.4$ $N$

Overcoming the force of static friction requires this parallel force plus $15$ $N$ , a total frictional force of $77.4$ $N$ .

$mu_s=(F_"frict")/(F_N)=77.4/62.4=1.24$

Once it is moving, keeping it moving only requires $7$ $N$ in addition to the parallel force, a total of $69.4$ $N$ .

$mu_k=(F_"frict")/(F_N)=69.4/62.4=1.11$

Coefficients of friction do not have units.

Science

Math

Humanities

... and beyond

An object with a mass of $9$ $9$ $k g$ $kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $15$ $15$ $N$ $N$ to start pushing the object down the plane and $7$ $7$ $N$ $N$ to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object with a mass of 999 kgkgkg is on a plane with an incline of - pi/4 −π4- pi/4 . If it takes 151515 NNN to start pushing the object down the plane and 777 NNN to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

Explanation:

Related questions

Impact of this question

An object with a mass of $9$ $9$ $k g$ $kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $15$ $15$ $N$ $N$ to start pushing the object down the plane and $7$ $7$ $N$ $N$ to keep pushing it, what are the coefficients of static and kinetic friction?