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# 3.4: Free-body Diagrams: Problem Solving

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### 3.4: Free-body Diagrams: Problem Solving

Free-body diagrams are essential tools for physicists and engineers studying the motion of objects. Free-body diagrams are graphical representations of the object or system under consideration, and they focus solely on the essential forces acting on the object. This tool helps break down complex problems into simpler models that are easier to understand and solve.

For example, consider a block with a mass of 10 kg released on an inclined plane at an angle of 30° to the horizontal, where the coefficient of friction is 0.2. The free-body diagram of this scenario displays the forces acting on the block, which include the gravitational force due to the weight of the block, the normal force acting perpendicular to the plane, and the frictional force. We can determine the resultant force the block experiences by understanding these forces.

When an object is placed on an inclined plane, the weight of the object has two components: one parallel to the slope and another perpendicular to the slope. The perpendicular component acts opposite to the normal force, and the net force in this direction is zero, as these two forces balance each other out. On the other hand, parallel to the slope, the weight has a non-zero component that causes the block to slide downward. The parallel component is the force that causes acceleration and opposes the resistance provided by the frictional force between the block and the surface. The frictional force opposes the object's motion, even when it is not moving. To calculate the frictional force, the normal force is multiplied by a coefficient of friction.

The net force is obtained by taking the difference between the gravitational force parallel to the slope and the frictional force. The value of the net force is substituted into Newton's second law of motion to obtain the acceleration value.