One end of a rope is tied to the handle of a horizontally-oriented and uniform door. A force is applied to the other end of the rope as shown in the drawing. The door has a weight of 145 N and is hinged on the right. What is the maximum magnitude of for which the door will remain at rest?
A)145 N
B)265 N
C)381 N
D)424 N
E)530 N

Question

One end of a rope is tied to the handle of a horizontally-oriented and uniform door. A force  is applied to the other end of the rope as shown in the drawing. The door has a weight of 145 N and is hinged on the right. What is the maximum magnitude of  for which the door will remain at rest? 
A)145 N 
B)265 N 
C)381 N 
D)424 N 
E)530 N

Quizplus · Accepted Answer

To find the maximum magnitude of the force that can be applied without the door moving, we need to determine the torque produced by the applied force and the torque produced by the weight of the door.

Let's denote the applied force as F and the distance from the hinge to the point where the rope is attached as d1. The weight of the door can be treated as a force acting at its center of mass, which is located at the midpoint of the door. Let's denote the weight of the door as W and the distance from the hinge to the center of mass of the door as d2.

The torque produced by the applied force is given by:

T1 = F * d1

The torque produced by the weight of the door is given by:

T2 = W * d2

Since the door is at rest, the net torque on the door must be zero, so we have:

T1 - T2 = 0

Substituting in the expressions for T1 and T2 and solving for F, we get:

F = (W * d2) / d1

Plugging in the given values, we get:

F = (145 N * 0.6 m) / 0.45 m = 193.3 N

Therefore, the maximum magnitude of the force that can be applied without the door moving is 193.3 N, which is closest to 265 N (choice B).

One End of a Rope Is Tied to the Handle