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A 1.4 kg block slides across a rough surface such that it slows down with an acceleration of 1.25 m/s(squared). What is the coefficient of kinetic friction between the block and the surface?
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MissPhiladelphia
F = ma 

where 

F = frictional force 
m = mass of the block = 1.4 kg (given) 
a = acceleration of the block = 1.25 m/sec^2 (given) 

Substituting values, 

F = (1.4)(1.25) 

F = 1.75 N 

By definition, 

F = (mu)(Normal force) 

where 

mu = coefficient of friction 
Normal force = mg = 1.4*9.8 = 13.72 

Again, substituting appropriate values, 

1.75 = mu(13.72) 

mu = 0.128

The coefficient of kinetic friction for the block k slides across a rough surface is 0.128.

What is Newtons second law of motion?

Newtons second law of motion shows the relation between the force mass and acceleration of a body.

It says, that the force applied on the body is equal to the product of mass of the body and the acceleration of it.

It can be given as,

[tex]F=ma[/tex]

Here, (m) is the mass of the body and (a) is the acceleration.

  • Step 1) Find the friction force-

As the mass of the block is 1.4 kg and the acceleration of it is 1.25 m/s (squared). Therefore the friction force can be given as using the above formula as,

[tex]F_f=1.4\times1.25\\F_f=1.75\rm N[/tex]

  • Step 2) Find the normal force-

The normal force acting on it due to gravity force is,

[tex]F_n=1.4\times9.8\\F_n=13.72\rm N[/tex].

  • Step 3) Find the coefficient of kinetic friction[tex](\mu)[/tex]-

Now the friction force acting on a moving body is equal to the product of normal force acting on it and the coefficient of kinetic friction.

Thus, the coefficient of kinetic friction[tex](\mu)[/tex] can be given as,

[tex]F_f=F_N\times\mu\\1.75=13.72\times \mu\\\mu=0.128[/tex]

Hence, the coefficient of kinetic friction for the block k slides across a rough surface is 0.128.

Learn more about the Newtons second law of motion here;

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