Question

A mass m1

is connected by a weightless cable passing over a frictionless pulley to a container of

water, whose mass is m0

(< m1

) at t = 0. If the container ejects water in downward direction at a

constant rate 1

 kgs

with a velocity 0

v relative to the container, then determine the acceleration of

m1

as a function of time.​

Answer 1

$\frac{m_{1}g - (m_{0} -1t)g + v_{0}1 }{m_{1} + (m_{0} - 1t) }$ is the acceleration of m1 as time's function.

Explanation:

Given that,

m_{0}  (< m1 ) at t = 0

Constant rate = 1 kg/s

velocity = $v_{0}$

To find:

Acceleration of m1 as time's function = ?

Procedure:

Mass at the opposite direction of the string = $(m_{0} - 1t)g$

$m_{1} g + 1v_{0} - (m_{0} - 1t)g$

= $(m_{1} + m_{0} - 1t) \frac{d_{v} }{d_{t}}$

∵ a = $\frac{m_{1}g - (m_{0} -1t)g + v_{0}1 }{m_{1} + (m_{0} - 1t) }$

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