Turning a doorknob through 0.53 of a revolution requires 0.10 J of work. What is the torque required to turn the doorknob?
(Average Torque) x (Angle in radians) = Work
Torque = 0.1/(2*pi*0.53) = ___ J
Well, torque is basically the love language between force and distance, my friend. To figure out the torque required to turn the doorknob, we need to know the force applied and the distance from the axis of rotation. Unfortunately, the given information doesn't quite cut it. So, let's just say that the torque required is directly proportional to the effort it takes to unleash your inner door-opening superhero. Keep turning that knob, caped crusader!
To find the torque required to turn the doorknob, we can use the equation:
Torque = Work / Angle
Given:
Work = 0.10 J
Angle = 0.53 revolution
Now, let's convert the angle from revolutions to radians:
1 revolution = 2π radians
So, 0.53 revolution = 0.53 * 2π radians
Now, we can calculate the torque:
Torque = Work / Angle
Torque = 0.10 J / (0.53 * 2π) radians
Calculating the value:
Torque = 0.10 J / (0.53 * 2 * 3.14159) radians
Torque ≈ 0.10 J / (3.33326) radians
Torque ≈ 0.0300 J/radians
Therefore, the torque required to turn the doorknob is approximately 0.0300 J/radians.
To find the torque required to turn the doorknob, we can use the equation:
Torque = Work / Angle
In this case, we are given the work required to turn the doorknob (0.10 J) and the angle through which the doorknob is turned (0.53 revolutions).
However, we need to convert the angle from revolutions to radians, as torque is typically measured in Newton-meters (Nm), and angles are most commonly measured in radians.
To convert revolutions to radians, we need to multiply the angle by 2π (since 1 revolution is equal to 2π radians).
Angle in radians = Angle in revolutions x 2π
Therefore, the angle in radians is:
Angle in radians = 0.53 revolutions x 2π
Now we can substitute the values into the equation:
Torque = Work / Angle
Torque = 0.10 J / (0.53 revolutions x 2π)
Simplifying the equation:
Torque = 0.10 J / (1.06π)
Calculating further:
Torque ≈ 0.094 Nm (rounded to three decimal places)
So, the torque required to turn the doorknob is approximately 0.094 Nm.