The suspension of mass M within a two-pulley system requires a force F. If pulley B is removed from the system, what is the ratio of the original value of the force with two pulleys to the new value of the force with one pulley?

Question

The suspension of mass M within a two-pulley system requires a force F.  If pulley B is removed from the system, what is the ratio of the original value of the force with two pulleys to the new value of the force with one pulley?

Quizplus · Accepted Answer

11ecba2d_1321_a7ea_a3bf_3930d92108cd_MD0008_00 Mechanical advantage describes the phenomenon by which forces are amplified using a mechanical device or system. One way to achieve mechanical advantage is by using a pulley system comprising a rope and one or more pulleys (ie, a wheel located on an axle) that may be configured to significantly reduce the force required to transport or support the weight (W) of an object. Pulley systems can include both fixed and load-sharing pulleys. Fixed pulleys do not contribute to mechanical advantage but redirect forces acting along the vertical axis. For example, an upward force may be converted into a downward force as a rope bends around a fixed pulley attached to the ceiling. In contrast, load-sharing pulleys are typically free to move up and down in accordance with the motion of the supported object, and the mechanical advantage of a pulley system is related to the number of load-sharing pulleys that are present. In this question, a force (F_original) is required to support the weight of mass M using a two-pulley system. Pulley A is fixed to the ceiling and therefore redirects the tension within the portion of the rope held by the user. Conversely, pulley B moves freely and acts to split the weight of the mass into two equal tension forces (T₁ and T₂). Tension force T₁ acts on the portion of the rope attaching pulley B to the ceiling, while tension force T₂ acts on the portion of the rope between pulley B and the user such that: 11ecba2d_1321_cefb_a3bf_73ec4ee08678_MD0008_00 As a result, the inclusion of pulley B within the system yields a mechanical advantage of two. Consequently, removing pulley B from the system will double the magnitude of force required to support the weight of the mass. 11ecba2d_1321_cefc_a3bf_0b850fcd460a_MD0008_00 Therefore, the ratio of the original force to the ratio of the new force (F_new) is 1:2 (Choice B). Educational objective: Mechanical advantage describes the force amplification that occurs through the use of a mechanical system or device. The mechanical advantage of pulley systems is related to the number of load-sharing pulleys but unrelated to the number of fixed pulleys that redirect forces.

The Suspension of Mass M Within a Two-Pulley System Requires