A 51.4 N force is applied to the outer edge of a door of width d = 2.72 m
a) Find the torque when the force acts perpendicular to the door.
N · m
(b) Find the torque when the force acts at an angle of è = 11.5° with respect to the door surface.
N · m
(c) Find the torque when the line of action of the force passes through the axis of the door hinges.
torque=force*2.72 give torque about hinges.
b. torque=force*2.72*sin11.5
c. zero.
To find the torque in each scenario, we can use the formula:
Torque = Force * Distance * sin(theta)
where:
- Force is the magnitude of the force applied,
- Distance is the distance from the force to the axis of rotation,
- theta is the angle between the force and the line connecting the force to the axis of rotation.
Let's calculate the torque for each scenario:
(a) When the force acts perpendicular to the door surface, sin(theta) = 1:
Torque = Force * Distance * sin(theta)
= 51.4 N * 2.72 m * 1
= 139.808 N · m
Therefore, the torque when the force acts perpendicular to the door is 139.808 N · m.
(b) When the force acts at an angle of è = 11.5° with respect to the door surface, we need to find the distance from the force to the axis of rotation. Since the force is applied at the outer edge of the door, the distance is equal to half of the door width:
Distance = d/2
= 2.72 m / 2
= 1.36 m
Torque = Force * Distance * sin(theta)
= 51.4 N * 1.36 m * sin(11.5°)
≈ 10.393 N · m
Therefore, the torque when the force acts at an angle of 11.5° with respect to the door surface is approximately 10.393 N · m.
(c) When the line of action of the force passes through the axis of the door hinges, the distance between the force and the axis of rotation becomes 0. Therefore, the torque in this case is:
Torque = Force * Distance * sin(theta)
= 51.4 N * 0 * sin(theta)
= 0 N · m
Therefore, the torque when the line of action of the force passes through the axis of the door hinges is 0 N · m.
To find the torque in each situation, we need to use the equation:
Torque = Force x Perpendicular Distance
a) When the force acts perpendicular to the door:
In this case, the perpendicular distance is equal to the width of the door, d. So we can calculate the torque as follows:
Torque = Force x Perpendicular Distance
= 51.4 N x 2.72 m
= 139.648 N·m
Therefore, the torque when the force acts perpendicular to the door is 139.648 N·m.
b) When the force acts at an angle of è = 11.5° with respect to the door surface:
In this case, the perpendicular distance is the distance from the hinge axis to the line of action of the force, represented by "r" in the diagram below:
---
| /
| /
d | / F
| /θ
|/
Using trigonometry, we can represent the perpendicular distance as:
Perpendicular Distance = d * sin(è)
Plugging in the values given in the problem, we can calculate the torque as follows:
Torque = Force x Perpendicular Distance
= 51.4 N x (2.72 m * sin(11.5°))
= 51.4 N x (2.72 m * 0.1989)
= 27.187808 N·m
Therefore, the torque when the force acts at an angle of è = 11.5° with respect to the door surface is approximately 27.19 N·m.
c) When the line of action of the force passes through the axis of the door hinges:
In this case, the perpendicular distance is zero because the force is acting directly along the axis of the door hinges. Therefore, the torque will also be zero:
Torque = Force x Perpendicular Distance
= 51.4 N x 0
= 0 N·m
Therefore, the torque when the line of action of the force passes through the axis of the door hinges is 0 N·m.