The Calculation of Torque Required to Remove a Stubborn Lug Nut
While attempting to remove a stubborn lug nut from a wheel on your project car, you apply a force on the end of a long wrench with length 18.5 cm, such that your arm and the wrench form a 90 degree angle. The lug nut isn't budging, so you start to push harder until it finally comes loose when you push with 212 N of force. How much torque was required to loosen the lug nut?
Calculation of Torque Required
The torque required to loosen the lug nut was approximately 39.22 Newton-meters. The torque required to loosen the lug nut can be calculated as follows:
Torque = Force x Distance
To calculate the torque required to loosen the lug nut, we need to calculate the distance between the point of application of force and the axis of rotation of the nut. This distance is the effective length of the wrench, which is the length of the wrench multiplied by the sine of the angle between the wrench and the force applied. So we have:
Effective length of wrench = 18.5 cm x sin 90°
Effective length of wrench = 18.5 cm
The torque required to loosen the lug nut is:
T = F x D
Effective torque = 212 N x 0.185 m
Effective torque = 39.22 Nm
Therefore, the torque required to loosen the lug nut is 39.22 Nm.
While attempting to remove a stubborn lug nut from a wheel on your project car, you apply a force on the end of a long wrench with length 18.5 cm, such that your arm and the wrench form a 90 degree angle. The lug nut isn't budging, so you start to push harder until it finally comes loose when you push with 212 N of force. How much torque was required to loosen the lug nut?
The torque required to loosen the lug nut was approximately 39.22 Newton-meters. The torque required to loosen the lug nut can be calculated by multiplying the force applied with the effective distance between the point of application of force and the axis of rotation. In this case, the effective length of the wrench is 18.5 cm, resulting in a torque of 39.22 Nm.