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A force of 18 N is applied horizontally to a 40 kg mass on a horizontal floor, causing it to accelerate at 0.3 m/s². Given g = 10 m/s², find the coefficient of kinetic friction.
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Answer
Step-by-step solution
4 stepsTo find the coefficient of friction, we need to apply Newton's Second Law.
Identify the given values.
- Applied Force () =
- Mass () =
- Acceleration () =
- Acceleration due to gravity () = (commonly used in such problems for simplicity, and it leads to one of the options exactly).
Calculate the normal force ().
Since the mass is on a horizontal floor, the normal force is equal to the gravitational force (weight) acting on the mass.
Apply Newton's Second Law in the horizontal direction to find the frictional force ().
The net force in the horizontal direction is the applied force minus the frictional force, and this net force causes the acceleration.
Now, solve for :
Calculate the coefficient of friction ().
The frictional force is related to the normal force by the coefficient of friction:
Rearrange to solve for :
The final answer is .
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