A 50 N force is applied to the end of a 30 cm wrench and makes an angle of 30 degrees with the handle of the wrench. What is the Torque on the bolt at the other end of the wrench? What direction does the Torque act? What is the Maximum and Minimum Torques and how are these accomplished?
Does the max occur at 90 degrees and the min occurs at 0 degrees?
I can't figure out the other answers.
Thanks
You might have to wait till a physics tutor comes on line.
The torque in the configuration you described is the lever arm length multiplied by the component of the force normal to the lever arm. That would be
50 N * 0.3 m * sin30 = 7.5 Newton meter..
With the same force and lever arm, the max torque would occur when the angle is 90 degrees. Your intuition is correct.
What is the torque on a bolt applied with a wrench that has a lever arm of 7.5 m with a force of 90 N?
To calculate the torque on the bolt at the other end of the wrench, you need to know both the magnitude of the force applied and the perpendicular distance from the point of rotation (in this case, the bolt) to the line of action of the force. The Torque (τ) can be calculated as follows:
τ = Force × Distance × sin(θ)
Where:
- τ is the torque
- Force is the applied force (in this case, 50 N)
- Distance is the perpendicular distance from the point of rotation to the line of action of the force (in this case, the length of the wrench, which is 30 cm or 0.3 m)
- θ is the angle between the force and the handle of the wrench (in this case, 30 degrees)
Plugging the values into the formula:
τ = 50 N × 0.3 m × sin(30°) = 7.5 Nm
So, the torque on the bolt at the other end of the wrench is 7.5 Nm.
The direction of the torque can be determined by the right-hand rule. If you curl your fingers in the direction the force is applied and your thumb points towards the handle of the wrench, then your palm will be facing towards the direction of the torque. In this case, the torque will be in the counterclockwise direction.
Regarding the maximum and minimum torques, you are correct that the maximum torque occurs when the force is applied perpendicular to the handle. In this case, that would be at 90 degrees. The minimum torque, which is zero, occurs when the force is applied parallel to the handle, at 0 degrees.