Question

A body slipping on a rough horizontal plane moves with a deceleration of 4 ms. The coefficient of
kinetic friction between the block and the plane is (g = 10 ms?)
​

Answer 1

Answer:

ANSWER

Let the mass be m.

Then on the horizontal surface, normal force is N=mg.

Hence friction is f =

$=μN=μmg</p><p></p><p></p><p>$

Hence deceleration is a

$\frac{f}{m} =μg</p><p></p><p></p><p>$

$</p><p>⟹μg=4⟹10μ=4</p><p></p><p></p><p>$

$⟹μ=0.4</p><p></p><p>$

Answer 2

Answer:

$\bigstar{\bold{\mu _k = 0.4}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Deceleration of the body (a)= 4 m/s²
• Acceleration due to gravity (g) = 10 m/s²

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Coefficient of kinetic friction ($\mu _k$)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let mass of the body be m

→ The coefficient of kinetic friction is given by the equation,

   $F_k = \mu _k \: F_n-----(1)$

→ Here $F_k$ is the force of kinetic friction and $F_n$ is the weight of the body.

→ $F_k$ is given by mass × acceleration

→ Substituting the datas we get,

  $F_k=m\times 4$

  $F_k=4\:m----(2)$

→ $F_n$ is given by mass × acceleration due to gravity

→ Substituting the datas,

   $F_n=m\times 10$

  $F_n=10\:m-----(3)$

→ Substitute equation 2 and 3 in equation 1

   $4\:m=\mu _k\times 10\:m$

→ Cancelling m on both sides

  $4=\mu _k\:10$

 $\mu _ k =4/10$

 $\mu _k = 0.4$

→ Hence the coefficient of kinetic friction is 0.4

  $\boxed{\bold{\mu _k = 0.4}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

The three types of friction are :

→ Static friction: The opposing force that comes into play when one body     tends to move on surface of another, but the actual motion has yet not started is called static friction

 $F_s=\mu _s\:mg$

→ Limiting friction : The maximum opposite force that comes into play when the body is just at the verge of moving over the surface of another body.

 $F_l=F_s(max)$

→Kinetic friction: It is the opposite force that comes into play when one body is actually moving over surface of another body

$F_k=\mu _k \: mg$