Question

A block of mass m placed on a rough horizontal
plane is pulled horizontally by a force giving
constant power po. If the maximum velocity of
block is vo, coefficient of friction is​

Answer 1

Given:

A block of mass m placed on a rough horizontal plane is pulled horizontally by a force giving constant power P_(0).

To find:

Coefficient of friction.

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(2, 2){\line(0, 1){2}}\put(2, 4){\line(1, 0){2}}\put(4, 4){\line(0, -1){2}}\put(4, 2){\line(-1, 0){2}}\put(3,3){\vector(1,0){2}}\put(3,3){\vector(-1,0){2}}\put(5,4){ \rm{F} }\put(1,4){ \rm{f} }\put(1,2){\line(1,0){4}}\put(3,3){\vector(0,1){2}}\put(4,5){ \rm{N} }\put(3,3){\vector(0,-1){2}}\put(4,1){ \rm{mg} }\end{picture}}$

Calculation:

Power can be expressed as the product of force and velocity such that ;

$\rm{P_{0} = (F) \times v_{0}}$

$= > \rm{P_{0} = ( \mu \times normal \: \: force) \times v_{0}}$

$= > \rm{P_{0} = ( \mu \times N) \times v_{0}}$

$= > \rm{P_{0} = ( \mu \times mg) \times v_{0}}$

$\rm{ = > \mu = \dfrac{P_{0}}{mgv_{0}} }$

So, final answer is:

$\boxed{ \rm{ \mu = \dfrac{P_{0}}{mgv_{0}} }}$