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In the given system with a frictionless pulley hanging from springs and a cable, where the pulley is equidistant between two supports, what will happen to the system if the distance between the supports (d) is increased?

a) The equilibrium position of the system will shift to the right.
b) The equilibrium position of the system will shift to the left.
c) The system will experience an increase in tension in the cable.
d) The system will experience a decrease in tension in the cable.

1 Answer

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Final answer:

Increasing the distance between supports in a frictionless pulley system is likely to decrease the tension in the cable due to changes in the cable's angle, which affects the vertical component balancing the load's weight.

Step-by-step explanation:

When considering a frictionless pulley system hung from springs with the pulley being equidistant between two supports, if the distance between the supports (d) is increased, it will not change the equilibrium position to the left or right, as that is determined by the downward force of gravity and the upward restoring force of the springs. However, increasing the distance (d) will lead to a change in the geometry of the system, and it is likely to decrease the tension in the cable because the angle of the cables with the horizontal will become more obtuse, reducing the vertical component of the tension that balances the weight of the load.

According to physics principles, the mechanical advantage (MA) of a pulley system is a measure of the force multiplication achieved by using a tool, mechanical device or machine system. The system's equilibrium is a state where the system is in balance, and there is no net force causing movement.

A key concept is that the tension in the cable of a pulley system remains constant throughout the cable. So, even with a change in the distance between the supports, this tension might adjust to maintain equilibrium, but the tension throughout the cable would not differ from one end to the other.

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