Question

Rank the design scenarios (A through F) on the basis of the tension in the supporting cable Rank from largest to smallest. To rank items as equivalent, overlap them.

Answer 1

The tension in the elevator cable depends on mass, acceleration, and gravity. A free-body diagram helps to visualize and calculate the tension. The scenario with the highest mass and acceleration when moving upward will have the highest tension.

Step-by-step explanation:

The ranking of tension in the supporting cables in scenarios A through F requires an understanding of how forces interact in a physical system. The amount of tension in the cable will depend on factors such as the mass of the elevator and its load, the acceleration of the elevator as it moves upwards, and the gravitational force acting on the system.

When an elevator starts from rest and accelerates upwards, the tension in the cable increases due to the added force required to accelerate the mass of the elevator and its load in addition to supporting the weight against gravity. A free-body diagram is essential in visualizing the forces at play and can help in establishing a clear and rigorous approach to calculating the tension in the cable. If the elevator's mass and acceleration are larger, the tension will also be larger.

Understanding that tension can have components due to the angle of forces, such as in a flexible connector or a tightrope walker scenario, is critical. If the tightrope walker's weight is perfectly balanced by the tension in the ropes, and the angles are the same on either side, the tensions in the ropes are equal. This principle can guide the student when considering different angles in design scenarios for ranking tension.

The significance of the tension in these scenarios often relates to the safety and structural integrity of systems like elevators or tightropes, making it a vital topic in engineering and physics applications.

Answer 2

To rank design scenarios based on supporting cable tension, considering elevator cables and tightrope walkers, we analyze the forces involved. Tension varies with mass, acceleration, and angles in static and dynamic situations. Trigonometry aids in calculating tension in equilibrium cases.

Step-by-step explanation:

To rank the design scenarios (A through F) based on the tension in the supporting cable, we need to consider the forces involved, particularly the tension resulting from an applied perpendicular force. In engineering scenarios such as elevator cables under tension or tightrope walkers balanced by wire tension, the tensile stress is not uniformly distributed and is affected by factors such as weight, angles, and forces.

If we consider elevator cables, for example, when the elevator starts from rest and accelerates upward, the tension in the cable is not just supporting the weight of the elevator and its load but also providing the force necessary for acceleration. A free-body diagram would help visualize these forces. To calculate the tension, we need to consider the mass (m), the gravitational force (g), and the acceleration (a). The tension, in this case, would be T = m(g + a).

In the case of a tightrope walker, the scenario involves static equilibrium where the tension in the wires must balance the weight of the person. If the wire angles are equal on both sides and the system is static, the tensions in the wires will be the same due to the lack of horizontal acceleration. Trigonometry can be used to calculate the tension on either side of the person. The tension would be larger the more horizontal the supporting wires.