The work required to screw a nut completely onto bolt, overcoming frictional resistance between the nut and bolt is 408 J. This is accomplished by applying a constant magnitude force onto the handle of a rachet at a position 20 cm from the nut. If the nut is completely secure after 20.3 turns, what magnitude of force is required to secure the nut?
Question
The work required to screw a nut completely onto bolt, overcoming frictional resistance between the nut and bolt is 408 J. This is accomplished by applying a constant magnitude force onto the handle of a rachet at a position 20 cm from the nut. If the nut is completely secure after 20.3 turns, what magnitude of force is required to secure the nut?
Solution
To solve this problem, we need to use the formula for work, which is Work = Force x Distance.
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First, we need to find the total distance the force is applied over. Since the nut is secured after 20.3 turns and the radius of the circle the force is applied in is 20 cm (or 0.2 m), the total distance is the circumference of the circle (2πr) multiplied by the number of turns.
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So, the total distance = 20.3 turns x 2π x 0.2 m = 25.468 m.
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Now, we can rearrange the formula for work to find the force. Force = Work / Distance.
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Substituting the given values into the formula gives us Force = 408 J / 25.468 m = 16.02 N.
So, the magnitude of the force required to secure the nut is approximately 16.02 N.
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