Question

If the coefficient of kinetic friction between a 22- kg crate and the floor is 0.30, what horizontal force is required to mive the crate at a steady soeed across the floor? what horizontal force is required if it is zero?

Answer 1

(a) Newton's second law states that the resultant of the forces acting on an object of mass m is equal to the product between the mass m and the acceleration a of the object:
$\sum F = ma$

In our case, there are two forces acting on the crate: the horizontal force F pushing the object and the friction force $\mu m g$, where $\mu$ is the friction coefficient. The crate is moving at steady speed, so its acceleration is zero: a=0, so Newton's second law becomes
$F-\mu m g=0$
So, the intensity of the horizontal force is
$F=\mu mg=(0.30)(22 kg)(9.81 m/s^2)=64.7 N$

(b) If the friction coefficient is zero, it means there is no friction force acting on the crate, so Newton's second law simply becomes
$F=0$
So, no force is needed to keep the crate at steady speed. 

Answer 2

Horizontal force to move the crate at a steady speed across the floor is 64.746 N

There is no horizontal force when coefficient of friction is zero.

Given :

Mass = 22 kg

Coefficient of friction = 0.30

a = 0, because crate moving at a steady speed.

Solution :

Horizontal force to move the crate at a steady speed across the floor is,

F = ma                   (According to Newton's second law)

$\rm F - \mu mg =0$          (since acceleration is zero)

$\rm F = 0.30\times 22 \times 9.81$

$\rm F = 64.746\;N$

Now, when coefficient of friction is zero than friction force is also zero. Therefore horizontal force is,

F = 0

So, there is no horizontal force when coefficient of friction is zero.

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