- #1

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- Homework Statement
- Two similar fixed pulleys with the arrangement as shown in diagram have the vertical string ends moving down at U m/s. If the string over pulley is inelastic then what would be the speed of mass M at any given instant of time?

- Relevant Equations
- Resolve velocity U in vertical and horizontal components

The way I tried to solve it is by using following reasoning.

The inclined part of the string will each have a speed of U m/s. So the point P just above mass M where the inclined strings meet is being moved up by each inclined string at ##U \cos {\theta} ##. Therefore, the speed of the point P is ##2U \cos {\theta} ##. This is not the correct answer, which is given as ##\dfrac {U} {\cos {\theta}} ##. Why is my reasoning not correct?

My attempt is as in screenshot below.

The inclined part of the string will each have a speed of U m/s. So the point P just above mass M where the inclined strings meet is being moved up by each inclined string at ##U \cos {\theta} ##. Therefore, the speed of the point P is ##2U \cos {\theta} ##. This is not the correct answer, which is given as ##\dfrac {U} {\cos {\theta}} ##. Why is my reasoning not correct?

My attempt is as in screenshot below.