calculate normal force exerted by the surface on the object.?

Question

An object is being pulled on a horizontal
surface with a horizontal force of 30 N.
If it is moving with a uniform speed and the coefficient
of friction between the sliding surfaces is 0.45,
calculate the normal force exerted by the surface on the object.
answer: 66.667 N

I know I have to calculate N but im not sure how to get there. The examples are nothing like this one.

Answer 1

Q: "An object is being pulled on a horizontal surface with a horizontal force of 30 N. If it is moving with a uniform speed and the coefficient of friction between the sliding surfaces is 0.45, calculate the normal force exerted by the surface on the object."



A: We're given that the object is in equilibrium -- "constant velocity" means that the net force is zero. Therefore the friction force must be equal and opposite to the (horizontal) applied force.



friction force Ff = 30 N.



But the friction force is equal to the normal force times the coefficient of friction, so

Ff = µ * Fn

where Fn is the normal force.



30 N = 0.45 * Fn

Fn = 30N / 0.45 = 66.667 N ◄ answer



Bonus: Since the surface and applied force are horizontal, we may conclude that the normal force is the weight of the object, and therefore its mass is

m = Fn / g = 66.667N / 9.8m/s² = 6.80 kg



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Answer 2

Since the object is moving at a uniform speed, the magnitude of the friction force must be equal to the horizontal force. Since the surface is horizontal, the following equation is used to determine the friction force.



Ff = μ * N

30 = 0.45 * N

N = 30 ÷ 0.465 = 66⅔ N

And since the surface is horizontal, the following equation is used to determine the friction force.



Ff = μ * m * g

30 = 0.45 * Weight

Weight = 66⅔ N

Answer 3

First of all, you know the this:



friction force = coefficient of friction x normal force.



Second of all, it tells you that the object is moving with uniform speed. That means acceleration is zero. That means the pulling force is not accelerating the object, which means the net force on the object is zero. That requires the friction force to be equal in magnitude to the friction force. So now you know the friction force.



So you have:



30N = 0.45 x normal force.



Solve for normal force.

Answer 4

The friction force resisting movement of the object is given by :



F sub f = ( muf ) ( N )



where muf is the coefficient of friction.



You then have :



N = ( F sub f ) / ( muf ) = ( 30 N ) / ( 0.45 ) = 66.7 N <--------------------