A force F = 59 N acts on a thin rod. Find the magnitude of the torque produced by this force about the indicated axis if 𝜃 = 56 degrees. Answer in Nm.
To find the magnitude of the torque produced by a force about a certain axis, you need to multiply the magnitude of the force by the perpendicular distance from the axis to the line of action of the force.
In this case, the force F = 59 N and 𝜃 = 56 degrees, so the line of action of the force makes an angle of 56 degrees with the axis.
Let's assume that the perpendicular distance from the axis to the line of action of the force is d meters.
To find d, we can use trigonometry. The perpendicular distance d is equal to the distance from the origin to the line of action of the force multiplied by the sine of the angle between the line of action of the force and the axis.
Let's say the distance from the origin to the line of action of the force is r meters.
Then, d = r * sin(𝜃).
Let's substitute the given values into the formula:
d = r * sin(56 degrees).
To find d, we need to know the value of r. If the rod is given in the problem, we can use its length as the value of r.
Once you have the value of d, you can calculate the torque by multiplying the magnitude of the force (F) by the perpendicular distance (d):
Torque = F * d.
Just substitute the given value of F and the calculated value of d into the formula to find the magnitude of the torque produced by the force.