A horizontal force of 10 N is applied to the outer edge of a door at an angle of 32° to the door, as shown in a view from the top looking down. The width of the door is 0.80 m. The magnitude of the torque of this force on the door with respect to the hinge is most nearly
2.4 N·m
0.4 N·m
8.0 N·m
4.2 N·m
5.3 N·m
4.2
Figure????
To find the torque of the force on the door with respect to the hinge, we need to use the formula:
Torque = Force x Perpendicular distance
From the given information, we have a horizontal force of 10 N applied at an angle of 32° to the door. To determine the perpendicular distance, we need to find the vertical component of this force.
Vertical component = Force x sin(angle)
Vertical component = 10 N x sin(32°)
Vertical component = 10 N x 0.52991926423
Vertical component ≈ 5.299 N
The perpendicular distance is the horizontal distance from the hinge to the line of action of the force. In this case, it is the width of the door, which is given as 0.80 m.
Now, we can calculate the torque:
Torque = 5.299 N x 0.80 m
Torque ≈ 4.239 N·m
Therefore, the magnitude of the torque of this force on the door with respect to the hinge is most nearly 4.2 N·m, which is the closest option provided.