As shown above an adhesive has been applied to contacting faces of two blocks so that the blocks interact with an adhesive force that has a magnitude, F_adhesion. A tension, T, is exerted by a wire attached to the upper blocks causing the blocks to remain at rest. The two blocks have weights, W_bottom and W_top. Which of the following must be true?
T=W_bottom+W_top+F_adhesion
T=W_top-F_adhesion
W_bottom=F_adhesion
W-top=T
The correct equation is: T = W_bottom + W_top + F_adhesion.
The correct statement is: T = W_bottom + W_top + F_adhesion.
This is because in order for the blocks to remain at rest, the tension in the wire must balance the combined weight of the bottom and top blocks (W_bottom + W_top). Additionally, the adhesive force (F_adhesion) must also be accounted for, as it contributes to the overall force keeping the blocks in place.
To determine which of the given options must be true, we need to understand the forces acting on the blocks and the conditions for them to remain at rest.
Let's analyze the forces acting on the blocks:
1. Weight (W_bottom and W_top): Each block experiences a downward force due to gravity, known as its weight. The weight is given by the mass of the block multiplied by the acceleration due to gravity (g).
2. Tension (T): The wire attached to the upper block applies a tension force in an upward direction to counterbalance the downward weight forces. This tension force keeps the blocks at rest.
3. Adhesive force (F_adhesion): The adhesive applied to the contacting faces of the blocks creates an interaction force between the blocks. This force opposes any separation between the blocks and acts parallel to the contacting surface.
To keep the blocks at rest, the following condition must be satisfied:
Sum of vertical forces = 0 (since the blocks are not accelerating vertically)
Now, let's evaluate the given options:
1. T = W_bottom + W_top + F_adhesion: This equation states that the tension force is equal to the sum of the weights and the adhesive force. However, this may not be true as the adhesive force could have a different direction or magnitude, affecting the equilibrium.
2. T = W_top - F_adhesion: This equation states that the tension force is equal to the weight of the top block minus the adhesive force. This equation could be true if the adhesive force opposes the tension force and the weight of the top block is greater than the adhesive force.
3. W_bottom = F_adhesion: This equation states that the weight of the bottom block is equal to the adhesive force. This equation cannot be true in general unless the adhesive force exactly counterbalances the weight of the bottom block.
4. W_top = T: This equation states that the weight of the top block is equal to the tension force. This equation is not generally true as the weight of the top block is typically greater than the tension force required for equilibrium.
Based on the analysis, option 2, T = W_top - F_adhesion, is the most likely to be true. However, it is important to note that the actual relationship between the forces depends on the specific conditions and parameters of the problem.