A 15 kg box is being pulled with a force of 45 N and is sliding with an acceleration of 2 m/s2. Find the coefficient of kinetic friction? (
Question
A 15 kg box is being pulled with a force of 45 N and is sliding with an acceleration of 2 m/s2. Find the coefficient of kinetic friction? (
Solution
Sure, let's solve this step by step:
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First, we need to find the force of friction. We can do this by using Newton's second law, which states that the force on an object is equal to its mass times its acceleration (F = ma). In this case, the force is 45 N, the mass is 15 kg, and the acceleration is 2 m/s². So, the force of the box is F = 15 kg * 2 m/s² = 30 N.
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The force pulling the box (45 N) is not only used to accelerate the box but also to overcome the friction. So, the force of friction is the difference between the pulling force and the force used to accelerate the box. Therefore, the force of friction (F_friction) is 45 N - 30 N = 15 N.
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The coefficient of kinetic friction (μk) is the ratio of the force of friction to the normal force. In this case, the normal force is equal to the weight of the box, which is its mass times the acceleration due to gravity (F_normal = m*g). Assuming the acceleration due to gravity is 9.8 m/s², the normal force is F_normal = 15 kg * 9.8 m/s² = 147 N.
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Now we can find the coefficient of kinetic friction by dividing the force of friction by the normal force: μk = F_friction / F_normal = 15 N / 147 N = 0.102.
So, the coefficient of kinetic friction is approximately 0.102.
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