Question

A pull of 180 N applied at 30 degrres to a rough horizontal plane just to move the body while a push of 220 N IS REQURIE ALONG SAME LINE OF ACTION TO MOVE THE SAME BODY CALCULCATE THE WEIGHT OF THE BODY AND COEFFICIENT OF FRICTION

Answer 1

Given:

A pull of 180 N applied at 30 degrres to a rough horizontal plane just to move the body while a push of 220 N is required along the same line of action to move the same body.

To find:

• Mass of body
• Coefficient of friction.

Calculation:

During Pull:

$\therefore180 \cos( {30}^{ \circ} ) = \mu \{mg - 180 \sin( {30}^{ \circ} ) \}$

During Push:

$\therefore220 \cos( {30}^{ \circ} ) = \mu \{mg + 220 \sin( {30}^{ \circ} ) \}$

Dividing the equations;

$= > \dfrac{220}{180} = \dfrac{mg + 220 \sin( {30}^{ \circ} ) }{mg - 180 \sin( {30}^{ \circ} ) }$

$= > \dfrac{11}{9} = \dfrac{mg + 220 ( \frac{1}{2} ) }{mg - 180 ( \frac{1}{2} ) }$

$= > \dfrac{11}{9} = \dfrac{mg + 110 }{mg - 90 }$

$= > 11mg - 990 = 9mg + 990$

$= > 2mg = 1980$

$= > 20m = 1980$

$\boxed{ = > m = 96 \: kg}$

Putting value of m ;

$\therefore180 \cos( {30}^{ \circ} ) = \mu \{mg - 180 \sin( {30}^{ \circ} ) \}$

$= > 180(0.86) = \mu \{96g - 180 ( \frac{1}{2} ) \}$

$= > 154.8= \mu \{960 - 90\}$

$= > 154.8= \mu \{870 \}$

$\boxed{ = > \: \mu = 0.17}$

Hope It Helps.