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, Fadhesion. 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, Wbottom and Wtop. Which of the following must be true?
(1 point)
Responses
T=Wbottom+Wtop+Fadhesion
upper T equals upper W subscript bottom baseline plus upper W subscript top baseline plus upper F subscript adhesion baseline
T=Wtop−Fadhesion
upper T equals upper W subscript top baseline minus upper F subscript adhesion baseline
Wbottom=Fadhesion
upper W subscript bottom baseline equals upper F subscript adhesion baseline
Wtop=T
None of the above statements must be true. The relationship between the tension, weights, and adhesive force is not defined in the given information.
The correct statement is:
T = Wbottom + Wtop + Fadhesion
Explanation:
- T represents the tension exerted by the wire.
- Wbottom represents the weight of the bottom block.
- Wtop represents the weight of the top block.
- Fadhesion represents the adhesive force between the blocks.
According to Newton's second law, for an object to remain at rest, the net force acting on it must be zero. In this case, the tension force T must balance the sum of the weights of the blocks (Wbottom and Wtop) and the adhesive force (Fadhesion). Therefore, the correct equation is T = Wbottom + Wtop + Fadhesion.
To determine which of the following statements must be true, we can analyze the forces acting on the system.
1. T = Wbottom + Wtop + Fadhesion: This equation states that the tension in the wire (T) is equal to the sum of the weight of the bottom block (Wbottom), the weight of the top block (Wtop), and the adhesive force (Fadhesion). This equation is correct because the tension in the wire must counterbalance the weight of both blocks as well as the adhesive force to keep the blocks at rest. Therefore, this statement is true.
2. T = Wtop - Fadhesion: This equation states that the tension in the wire (T) is equal to the difference between the weight of the top block (Wtop) and the adhesive force (Fadhesion). This equation is not correct because the tension in the wire should result from the total weight of both blocks and the adhesive force, not just the weight of the top block. Therefore, this statement is false.
3. Wbottom = Fadhesion: This equation states that the weight of the bottom block (Wbottom) is equal to the adhesive force (Fadhesion). This equation is not correct because the weight of the bottom block is only one component that contributes to the total tension in the wire. Therefore, this statement is false.
4. Wtop = T: This equation states that the weight of the top block (Wtop) is equal to the tension in the wire (T). This equation is not correct because the weight of the top block alone does not account for the adhesive force or the weight of the bottom block, both of which contribute to the total tension. Therefore, this statement is false.
Based on the analysis, the only statement that must be true is T = Wbottom + Wtop + Fadhesion.