To tighten a bolt, you push with a force of 84N at the end of a wrench handle that is 0.24m from the axis of the bolt.
If you move your hand inward to be only 0.10 m from the bolt, find the force that you should exert to achieve the same torque.
2.4*84
To find the force that you should exert to achieve the same torque when you move your hand inward, you need to understand the concept of torque and how it is related to force and distance.
Torque is the measure of a force's tendency to cause an object to rotate about an axis. Mathematically, torque is calculated as the product of the force and the distance from the point of rotation to the line of action of the force. This relationship is given by the equation:
Torque (τ) = Force (F) × Perpendicular distance (r)
In this case, the torque about the bolt is the same in both scenarios, so we can set the torques equal to each other:
Torque1 = Torque2
The torque in the first scenario is given by:
Torque1 = Force1 × Distance1
Where Force1 is the force applied at a distance of 0.24m from the bolt.
The torque in the second scenario is given by:
Torque2 = Force2 × Distance2
Where Distance2 is the new distance of 0.10m from the bolt.
Since the torques are equal, we can equate the two equations:
Force1 × Distance1 = Force2 × Distance2
Plugging in the given values:
84N × 0.24m = Force2 × 0.10m
Now, we can solve for Force2:
Force2 = (84N × 0.24m) / 0.10m
Force2 = 201.6N
Therefore, to achieve the same torque when your hand is moved inward to be only 0.10m from the bolt, you should exert a force of 201.6N.
To find the force that you should exert to achieve the same torque when you move your hand inward to be only 0.10 m from the bolt, you can use the principle of torque.
Torque is given by the formula: Torque = force * lever arm
The initial torque when you push with a force of 84N at a distance of 0.24m from the axis of the bolt can be calculated as follows:
Initial torque = 84N * 0.24m
To achieve the same torque when you move your hand inward to be only 0.10m from the bolt, we can rearrange the formula for torque and solve for the force:
New torque = force * 0.10m
Since the initial and new torques are equal, we have:
84N * 0.24m = force * 0.10m
Simplifying the equation:
2.016 = force * 0.10
Dividing both sides by 0.10:
force = 2.016 / 0.10
Calculating:
force = 20.16N
Therefore, to achieve the same torque when you move your hand inward to be only 0.10m from the bolt, you should exert a force of approximately 20.16N.