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?
Instead of 90 degrees to the shaft (optimal) You are at 120 which is 30 degrees off.
so your force perpendicular to the shaft is
F cos 30
The torque is F cos 30 * 0.39
so
F cos 30 * 0.390 = 49.0
To solve this question, you can use the concept of torque and the equation τ = F * r * sinθ, where τ represents the torque, F is the force applied, r is the distance from the axis of rotation to the point where the force is applied, and θ is the angle between the force vector and the line connecting the axis of rotation to the point of force application.
In this case, you are given the torque (τ) and need to find the force (F). You are also provided with the length of the torque wrench (r = 39.0 cm = 0.39 m) and the angle (θ = 120°).
1. Convert the angle from degrees to radians:
θ (radians) = θ (degrees) * π/180
θ (radians) = 120° * π/180 = 2.094 radians
2. Rearrange the torque equation to solve for force (F):
F = τ / (r * sinθ)
3. Substitute the given values into the equation to calculate the force:
F = 49.0 N m / (0.39 m * sin(2.094))
F ≈ 49.0 N m / (0.39 m * 0.866)
F ≈ 140.7 N
Therefore, you need to apply a force of approximately 140.7 N to tighten the lug nut to the specified torque.