A force of 200 N pulls a sledge of mass 50 kg and overcomes a frictional force of 40 N. What is the acceleration of the sledge?

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Points to Remember:

  • Newton’s Second Law of Motion (F = ma)
  • Net force calculation
  • Units of measurement (Newtons, kilograms, meters per second squared)

Introduction:

This question requires a factual and analytical approach to determine the acceleration of a sledge given its mass, the pulling force, and the frictional force acting upon it. The core principle involved is Newton’s Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). Understanding this law and how to apply it to a real-world scenario is crucial for solving this problem.

Body:

1. Identifying Forces:

The problem presents two significant forces acting on the sledge:

  • Applied Force (Fa): A pulling force of 200 N. This force acts in the direction of motion.
  • Frictional Force (Ff): A resistive force of 40 N. This force acts opposite to the direction of motion.

2. Calculating Net Force:

To determine the acceleration, we need to find the net force acting on the sledge. This is the difference between the applied force and the frictional force:

Net Force (Fnet) = Fa – Ff = 200 N – 40 N = 160 N

3. Applying Newton’s Second Law:

Newton’s Second Law (F = ma) allows us to calculate the acceleration (a) of the sledge. We know the net force (Fnet = 160 N) and the mass (m = 50 kg). Rearranging the formula to solve for acceleration, we get:

a = Fnet / m = 160 N / 50 kg = 3.2 m/s²

4. Result:

Therefore, the acceleration of the sledge is 3.2 meters per second squared (3.2 m/s²). This means that the sledge’s velocity increases by 3.2 meters per second every second.

Conclusion:

In summary, by applying Newton’s Second Law of Motion and considering both the applied force and the frictional force, we determined that the sledge accelerates at 3.2 m/s². This problem highlights the importance of understanding vector quantities (forces have both magnitude and direction) and how to calculate net force to accurately predict the motion of an object. Further analysis could involve exploring different surface materials and their impact on frictional forces, or investigating the effect of varying applied forces on the sledge’s acceleration. A deeper understanding of these principles is crucial for advancements in fields like engineering and physics, leading to safer and more efficient designs and systems.

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