A 80-N force is applied to the end of a 50-cm wrench and makes an angle of 45° with the handle of the wrench.
a) What is the torque on a bolt at the other end of the wrench?
b) What is the maximum torque that can be exerted by a 100-N force on this wrench and how can it be achieved?
component of force perpendicular to handle = 80 cos 45
lever arm = 0.050 meters
torque = (80 cos 45)* 0.050
100 * .050 perpendicular to arm of wrench
sorry, 50 cm = 0.50 meters
(80 cos 45)* 0.50
and
100 * 0.50 perpendicular to arm of wrench
To find the torque, we need to know both the force applied and the distance from the point of rotation.
a) To find the torque on the bolt at the other end of the wrench, we can use the formula: torque = force * distance. The distance here refers to the perpendicular distance from the point of rotation to the line of action of the force.
In this case, the force applied is 80 N. However, we need to find the perpendicular distance. Since the angle between the force and the handle of the wrench is 45°, we can break the force into its components: one parallel to the handle and one perpendicular to the handle.
The perpendicular component of the force is given by: force perpendicular = force * sin(angle). So, force perpendicular = 80 N * sin(45°).
Next, given that the length of the wrench is 50 cm = 0.5 m, the perpendicular distance from the point of rotation to the line of action of the force is half the length of the wrench. So, the distance in this case is 0.5 m / 2 = 0.25 m.
Now, we can calculate the torque by multiplying the force perpendicular by the distance: torque = force perpendicular * distance = (80 N * sin(45°)) * 0.25 m.
b) To find the maximum torque that can be exerted by a 100-N force on this wrench and how it can be achieved, we need to analyze the angle at which the force should be applied.
The maximum torque is obtained when the force is applied perpendicular to the handle of the wrench. This means that the angle between the force and the handle of the wrench should be 90°.
Using the same formula as before, torque = force * distance, with force = 100 N and distance = 0.5 m / 2 = 0.25 m, we can calculate the maximum torque by multiplying the force by the distance.
So, the maximum torque that can be exerted by a 100-N force on this wrench is: torque = 100 N * 0.25 m. To achieve this maximum torque, the force should be applied perpendicular to the handle of the wrench, which means the angle between the force and the handle should be 90°.