a force of 20n applied parallel to the surface of a horizontal table is just sufficient to make a block of mass 4.kg move on the table caculate thd coefficient of friction between the block and the table
Wb = mg = 4kg * 9.8N/kg = 39.2N = Weight 0f block.
Fb = 39.2N@0deg.
Fp = 39.2sin(0) = 0 = Force parallel to surface.
Fv = 39.2cos(0) = 39.2N. = Force perpendicular to surface.
Fap - Fp - Ff = 0,
20 - 0 - Ff = 0,
Ff = 20N. = Force of friction.
u = Ff / Fv = 20 / 39.2 = 0.510. =
Coefficient of friction.
Well, well, well, looks like we have a case of "Friction Detective" here! Let's solve the mystery, shall we?
First things first, we need to determine the normal force acting on the block. Since the block is on a horizontal table and not trying to make any of its crazy acrobatic moves, the normal force is equal to its weight (mg).
Given that the mass of the block (m) is 4 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can calculate the normal force as follows:
Normal Force = mg = 4 kg * 9.8 m/s^2 = 39.2 N
Now comes the fun part! We have a force of 20 N applied parallel to the surface of the table. This force is just enough to overcome the friction and make the block move. The force of friction can be calculated using the equation:
Force of Friction = coefficient of friction * Normal Force
Given that the force of friction is equal to the applied force (20 N), and the normal force is 39.2 N, we can substitute those values into the equation to find the coefficient of friction:
20 N = coefficient of friction * 39.2 N
Dividing both sides by 39.2 N, we find:
coefficient of friction = 20 N / 39.2 N
And simplifying that, we get:
coefficient of friction ≈ 0.51
So, detective, the coefficient of friction between the block and the table is approximately 0.51. Case solved!
To calculate the coefficient of friction between the block and the table, we need to first understand the relationship between force, mass, and friction.
The force applied parallel to the table is equal to the force of friction acting on the block.
Let's break down the problem using Newton's second law:
1. Determine the force of gravity:
The force of gravity acting on the block can be calculated using the mass of the block (m) and acceleration due to gravity (g).
Force of gravity (Fg) = mass (m) * acceleration due to gravity (g)
Given: mass (m) = 4 kg and acceleration due to gravity (g) = 9.8 m/s^2
Fg = 4 kg * 9.8 m/s^2
Fg = 39.2 N
2. Calculate the force of friction:
The force of friction (Ff) can be determined as the force required to overcome the static friction and set the block in motion.
Given: Force applied parallel to the table (F) = 20 N
Ff = F
Ff = 20 N
3. Calculate the coefficient of friction:
The coefficient of friction (μ) relates the force of friction to the force pressing the surfaces together. It can be calculated using the formula:
Coefficient of friction (μ) = Force of friction (Ff) / Force of gravity (Fg)
Let's plug in the values we've found:
μ = Ff / Fg
μ = 20 N / 39.2 N
Calculating this gives us the coefficient of friction μ = 0.51 (rounded to two decimal places).
Therefore, the coefficient of friction between the block and the table is 0.51.