Help Needed Please...
After changing a tire on your car, you need to tighten one of the lug nuts to the proper specified torque of 49.0 N m. How much force is needed if you're pushing down on the end of the 39.0 cm long torque wrench at an angle of 120° with respect to the wrench shaft?
Please I need help on how to go about solving this question?
http://www.jiskha.com/display.cgi?id=1449174010
To solve this question, you can use the concept of torque. Torque is defined as the product of force and the perpendicular distance from the point of rotation to the line of action of the force. In this case, the point of rotation is the lug nut, and you need to find the force required to achieve the specified torque of 49.0 N m.
To calculate the force, you can use the following formula:
Torque = Force × Distance × sin(θ)
Where:
- Torque is the desired torque of 49.0 N m
- Distance is the length of the torque wrench, which is given as 39.0 cm (0.39 m)
- θ is the angle between the force and the wrench shaft, given as 120°
Rearranging the formula, we can solve for force:
Force = Torque / (Distance × sin(θ))
Substituting the given values:
Force = 49.0 N m / (0.39 m × sin(120°))
Now, let's calculate the force:
Force = 49.0 N m / (0.39 m × 0.866)
Force = 173.3 N
Therefore, to tighten the lug nut to the specified torque, a force of approximately 173.3 N is needed when pushing down on the end of the torque wrench.