A force of 50N acts on the end of a wrench 18 cm long.
a) In what direction should the force act to produce the maximum torque? Draw
a diagram.
b) What is the maximum torque? (State both magnitude and direction)
a) Well, to produce the maximum torque with a wrench, the force should be applied perpendicular to the wrench, parallel to the handle. So if you're holding the handle of the wrench like a ninja warrior, the force should be in the direction of your karate chop!
b) The maximum torque can be calculated using the formula: Torque = force × distance. In this case, the force is 50N and the distance is 18 cm. So the maximum torque would be 900 N⋅cm (or you can convert it to N⋅m if you prefer fewer centimeters in your life). The direction of the torque depends on the orientation of the wrench, but imagine it twisting clockwise like a corkscrew trying to open a stubborn bottle of pickles.
a) The force should act perpendicular to the wrench in order to produce the maximum torque. Torque is maximized when the force and the line of action of the force are at 90 degrees to each other. Here is a diagram illustrating the direction of the force:
```
|
|
|-------
| F
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|
```
b) To find the maximum torque, we need to calculate the moment arm, which is the perpendicular distance between the line of action of the force and the axis of rotation. In this case, the moment arm is equal to the length of the wrench, 18 cm, or 0.18 m.
Torque (τ) is calculated by multiplying the force (F) by the moment arm (r):
τ = F * r
Substituting the given values:
τ = 50 N * 0.18 m
Calculating the torque:
τ = 9 Nm
Therefore, the maximum torque is 9 Nm, and its direction is perpendicular to the plane of the wrench.
To determine the direction that the force should act to produce the maximum torque, we need to understand the concept of torque. Torque is the measure of the turning force around an axis or pivot point. It depends on both the magnitude of the force applied and the distance from the pivot point to where the force is applied.
a) In order to produce the maximum torque, the force should act perpendicular (or at a 90-degree angle) to the length of the wrench. This can be illustrated with a diagram:
```
|
|---->[Force]
|
|
|---------->[Pivot Point]
|
|
|
[Wrench]
```
In the diagram, the force is represented by an arrow, which should be drawn perpendicular to the wrench's length. The pivot point is denoted by a dot.
b) To calculate the maximum torque, we need to multiply the force applied by the distance from the pivot point to where the force is applied. Here, the force is 50N. The distance is given as 18 cm, but it is recommended to convert it to meters for consistent units.
Distance = 18 cm = 18/100 m = 0.18 m
Torque = Force x Distance = 50N x 0.18m = 9 Nm
Therefore, the maximum torque is 9 Nm, and its direction would be perpendicular to the length of the wrench.