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A weight with mass ????w=250 gmw=250 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius ????=3.00 cmR=3.00 cm and mass ????s=100 gMs=100 g . Find the magnitude of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.

Respuesta :

Answer:

[tex]a = 8.175 m/s^2[/tex]

Explanation:

The mass is connected with a string and wrapped around the spool

So here we can say that the force on the mass is due to weight and the tension in string so as per the force equation we have

[tex]mg - T = ma[/tex]

now for the spool we can say it is rotated due to the tension force on it

so we can say

[tex]TR = I\alpha[/tex]

[tex]TR = (\frac{1}{2}m_s R^2)(\frac{a}{R})[/tex]

[tex]T = \frac{1}{2}m_s a[/tex]

now we have

[tex]mg - \frac{1}{2}m_s a = ma[/tex]

[tex]mg = a(\frac{1}{2}m_s + m)[/tex]

now the acceleration is given as

[tex]a = \frac{mg}{\frac{1}{2}m_s + m}[/tex]

now plug in values of all masses

[tex]a = \frac{0.250(9.81)}{\frac{1}{2}(0.100) + 0.250}[/tex]

[tex]a = 8.175 m/s^2[/tex]

shubhamchouhanvrVT

The Magnitude of the acceleration when a mass descends will be

[tex]a=8.175\dfrac{m}{s^2}[/tex]

What will be the acceleration of the mass?

It is given that

Mass m= 250gm

spoon radius r=3cm

and weight = 100gm

Since the mass is tied by a rope and this rope is wrapped on the spoon

by balancing the force from newtons law

[tex]mg-T=ma[/tex]

[tex]Tr=I\alpha[/tex]

[tex]Tr=\dfrac{1}{2} m_{s}R^{2}(\dfrac{a}{R})[/tex]

[tex]Tr=\dfrac{1}{2}m_{s}a[/tex]

now we have

[tex]mg-\dfrac{1}{2} m_{s}a=ma[/tex]

[tex]mg=a(\frac{1}{2} m_{s}+m)[/tex]

now the acceleration is given as

[tex]a=\dfrac{m_{g}}{\frac{1}{2} m_{s}+m}[/tex]

[tex]a=\dfrac{0.25(0.981)}{\dfrac{1}{2}(0.1)+0.250 } =8.175\frac{m}{s^2}[/tex]

Thus the Magnitude of the acceleration when a mass descends will be

[tex]a=8.175\dfrac{m}{s^2}[/tex]

To know more about acceleration follow

https://brainly.com/question/25545050

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