A person tries to lock the door by putting a brick in Case-1 and a small wooden piece in Case-2. Which of the following forces gives a torque about the rotation axis of the door that opposes the torque of the force by the person trying to open the door in Case-1 ? a. the normal force by the brick on the door b. the frictional force by the brick on the door c. the weight of the door d. the weight of the brick
Answers
Explanation:
Several familiar factors determine how effective you are in opening the door. See Figure 1. First of all, the larger the force, the more effective it is in opening the door—obviously, the harder you push, the more rapidly the door opens. Also, the point at which you push is crucial. If you apply your force too close to the hinges, the door will open slowly, if at all. Most people have been embarrassed by making this mistake and bumping up against a door when it did not open as quickly as expected. Finally, the direction in which you push is also important. The most effective direction is perpendicular to the door—we push in this direction almost instinctively.
In the figure, six top views of a door are shown. In the first figure, a force vector is shown in the North West direction. The perpendicular distance of the force from the point of rotation is r. In the second figure, a force is applied in the opposite direction at the same distance from the hinges. In the third figure, a smaller force in applied at the same point. In the next figure, a horizontal force is applied at the same point. In this case, the perpendicular distance from the hinges is shown as r sin theta. In the next figure, force is applied at a distance near the hinges. In the final figure, the force is shown along the direction of hinges toward the handle of the door.
Figure 1. Torque is the turning or twisting effectiveness of a force, illustrated here for door rotation on its hinges (as viewed from overhead). Torque has both magnitude and direction. (a) Counterclockwise torque is produced by this force, which means that the door will rotate in a counterclockwise due to F. Note that r⊥ is the perpendicular distance of the pivot from the line of action of the force. (b) A smaller counterclockwise torque is produced by a smaller force F′ acting at the same distance from the hinges (the pivot point). (c) The same force as in (a) produces a smaller counterclockwise torque when applied at a smaller distance from the hinges. (d) The same force as in (a), but acting in the opposite direction, produces a clockwise torque. (e) A smaller counterclockwise torque is produced by the same magnitude force acting at the same point but in a different direction. Here, θ is less than 90º. (f) Torque is zero here since the force just pulls on the hinges, producing no rotation. In this case, θ = 0º.
The magnitude, direction, and point of application of the force are incorporated into the definition of the physical quantity called torque. Torque is the rotational equivalent of a force. It is a measure of the effectiveness of a force in changing or accelerating a rotation (changing the angular velocity over a period of time). In equation form, the magnitude of torque is defined to be
τ
=
r
F
sin
θ
where τ (the
Answer: The answer will be (d) the weight of the brick.
Explanation: When a person tries to lock the door using a brick it's the weight of the brick which offers opposition to the torque of the force by the person trying to open the door.
The above statement can be justified by the following reasons:
- Newton's First Law of Motion
According to the law, every body retains its state of inertia until and unless an external force is applied to it.
In this case, the brick used to close the door will retain it's inertia of rest as long as the force is applied to move it.
Hence, the person trying to open the door first has to apply force to move the stone along with the force applied to open the door.
- Newton's Third Law of Motion.
According to the law, every action has an equal and opposite reaction.
In this case, the person applying force towards the door and the brick applying the force opposing to this force due to its mass. This makes it a tough task for the person to open the door.
In order to open the door the person must apply such amount of force which can over come the force of inertia of the brick to open the door.