Dinámica-Ejemplo 13-Determinar el coeficiente de fricción dinámico.

Dynamic Friction Coefficient Calculation

Introduction to the Problem

• The problem involves a block weighing 40 N subjected to a force of 15 N at an angle of 25 degrees with the horizontal, resulting in an acceleration of 1.5 m/s².

Steps to Determine Dynamic Friction Coefficient

• The goal is to calculate the dynamic friction coefficient using a free body diagram (FBD). A Cartesian plane is established for analysis.

Forces Acting on the Block

• Key forces include:

• Applied force (15 N at 25 degrees).

• Weight of the block acting downward (40 N).

• Normal force acting upward.

• Frictional force opposing motion.

Force Components and Equations

• The applied force is decomposed into two components:

• F_y = F cdot sin(25^circ)

• F_x = F cdot cos(25^circ)

• Since there’s no vertical movement, the sum of forces in the y-direction equals zero.

Analyzing Forces in Y-Direction

• The equation for forces in the y-direction includes:

• Normal force (positive).

• Vertical component of applied force ( +F_y ).

• Weight ( -W ) acting downwards.

• This leads to:

[ N + F_y - W = 0 ]

Solving for Normal Force

• Rearranging gives:

[ N = W - F_y ]

• Substituting values results in calculating F_y = 6.34 N, leading to a normal force N = 33.66 N.

Calculating Frictional Force

• To find frictional force, apply Newton's second law in x-direction where acceleration exists:

[ F_net = m cdot a]

• Mass is calculated as:

[ m = W/g = 40N/9.8m/s^2 ≈4.08 kg]

Forces in X-Direction Analysis

• In x-direction, we have:

[ F_x (positive direction) – f_friction (negative direction)= ma]

Calculating the Coefficient of Friction

Steps to Calculate Friction Force

• The initial calculation involves determining the force using the equation 15 times cos(25^circ), resulting in a friction force of approximately 13.59 N.

• A secondary calculation is performed by multiplying 4.08 times 1.5, yielding a value of 6.12 N, which is then subtracted from the previous result.

• The final friction force calculated is 7.47 N, representing the total frictional force acting on the object.

Determining the Coefficient of Friction

• To find the coefficient of friction, it is defined as the ratio of frictional force to normal force: textCoefficient = fractextFriction ForcetextNormal Force .

• Substituting values into this formula gives 7.47/33.66 , leading to further calculations for accuracy.

Resulting Coefficient Value

• The dynamic coefficient of friction calculated from these values is approximately 0.22.

• It’s noted that this coefficient does not have any units associated with it, indicating a pure ratio result.