find the frictional force exerted on a 20kg block pulled slowly over a horizontal floor using a rope which makes a 30 degree angle over the horizontal. the pulling force is 100N???

i found the Fn to be 146 N what do i do from there?

You want the frictional force, not the normal force.

100* cos 30 = 86.6 N
is the frictional force, since it is being pulled slowly and presumably not acclerating. You don't need to use the mass information to get that.

The normal force is
M g - 100N sin 30 = 146 N; you were right about that.

The coefficient of sliding friction is 86.6/146 = 0.59

To find the frictional force exerted on the block, we need to use the equation for the frictional force:

Ff = μ * Fn

Where:
Ff is the frictional force
μ is the coefficient of friction
Fn is the normal force

You mentioned that you found the normal force (Fn) to be 146 N, which is correct. Now we need to find the coefficient of friction (μ).

To find μ, we can use the given information about the pulling force and the angle of the rope. In this scenario, the force of tension in the rope can be broken down into two components: the vertical component (Fv) and the horizontal component (Fh).

The vertical component (Fv) of the tension force can be found using trigonometry:

Fv = Ft * sin(θ)

Where:
Ft is the total tension force in the rope
θ is the angle of the rope with respect to the horizontal

In this case, Ft is 100 N and θ is 30 degrees, so:

Fv = 100 N * sin(30°) = 50 N

The vertical component (Fv) of the tension force counteracts the force of gravity pulling the block downward. So, we can find the normal force (Fn) by subtracting Fv (50 N) from the weight of the block.

Fn = weight - Fv

Since the weight of the block is given by:

weight = mass * gravitational acceleration

And the mass is 20 kg, and the gravitational acceleration is approximately 9.8 m/s², we can calculate:

Fn = 20 kg * 9.8 m/s² - 50 N
Fn = 196 N - 50 N
Fn = 146 N

So, you have already correctly determined that the normal force (Fn) is 146 N.

Now that we have both the normal force (Fn) and the pulling force (Ft), we can substitute them into the frictional force equation:

Ff = μ * Fn

Since the problem does not give a specific value for the coefficient of friction (μ), we cannot calculate the frictional force without that information. The coefficient of friction depends on the materials in contact (e.g., the block and the floor). It would need to be given or determined experimentally.