A brick rests on a table. A cord is attached to the brick and a tension force, T, is exerted on the brick by the cord. The magnitude and direction of the normal force of the desk on the brick is equal to
a) Wbrick + Tcos θ
b) Wbrick - Tcos θ
c) Wbrick - Tsin θ
d) Wbrick + Tsin θ
I assume the cord is pulling up (against gravity), so (b) or (c) would seem to be the logical choice. So which would it be?
To determine the magnitude and direction of the normal force of the desk on the brick, we first need to understand the concept of the normal force.
The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular (or normal) to the surface. In this case, the surface is the table, and the object resting on it is the brick.
Now, let's analyze the forces acting on the brick. The two forces acting on the brick are the tension force, T, exerted by the cord, and the weight of the brick, denoted as Wbrick.
Since the brick is at rest on the table, the net force acting on it must be zero in both the horizontal and vertical directions. In other words, the vertical component of the tension force should balance the weight, and the horizontal component of the tension force should be balanced by another force.
The weight of the brick, Wbrick, acts vertically downwards. Therefore, the vertical component of the tension force can be expressed as T * cos θ, where θ is the angle between the cord and the vertical direction. This vertical component should balance the weight, so the normal force of the desk on the brick needs to be equal in magnitude but acting in the opposite (upwards) direction.
Hence, the correct answer is:
a) Wbrick + T * cos θ