Posted by **Anonymous** on Sunday, May 13, 2012 at 12:15am.

A block of mass m lies on a rough plane which is inclined at an angle è to the horizontal. The coefficient of static friction between the block and the plane is ì. A force of magnitude P is now applied to the block in a horizontal direction, towards the plane.

Show that the minimum value of P which is necessary to ensure that the block remains at rest on the plane, is

P=[mg(sinè-ìcosè)]/(ìsinè+cosè)

Please help! Thanks!

- Physics -
**Elena**, Sunday, May 13, 2012 at 12:15pm
Take x-axis directed along the incline downwards, and y-axis directed normaly away from the incline.

Projections of the equation of motion on the x- and y- axes are:

m•g•sinα - P•cosα – F(fr) = 0,

-m•g•cos α + N -P•sinα = 0.

F(fr) = μ •N = μ •(m•g•cos α+P•sinα).

0 = m•g•sinα - P•cosα - μ •(m•g•cos α+P•sinα) =

= m•g•sinα - P•cosα - μ •m•g•cos α+μ•P•sinα.

P = m•g•( sinα - μ•cos α)/(cos α + μ•sinα).

## Answer This Question

## Related Questions

- Physics - A block P of mass 2.75 kg is lying on a rough inclined plane of angle...
- physics - A block of mass 39 kg lies on an inclined plane, as shown. The ...
- Physics - This is the info for the problem: A block of mass M1 = 160.0 kg sits ...
- Physics - A block with mass m1 on a plane inclined at angle to the ...
- physics - A block of mass m is initially at rest at the top of an inclined plane...
- Physics - A block of mass 0.5 kg rests on a smooth inclined plane. It is then ...
- Physics - A block slides down an inclined plane that makes an angle of 23° with ...
- physical - A block with mass m1 on a plane inclined at angle ƒÑ to the ...
- Physics - A 54.0kilogram block is placed on a plane that is inclined 32 degrees ...
- Physics - A 4 kg block slides down a rough inclined plane inclined at 30° with ...

More Related Questions