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A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum speed can the mass have if the string is not to break?

Respuesta :

cjmejiab

To solve this problem we will apply the concepts given from the circular movement of the bodies for which we have that the centripetal Force is defined as a product between the mass and the velocity squared at the rate of rotation, mathematically this is

[tex]F_c = \frac{mv^2}{r}[/tex]

Where,

m = Mass

v = Velocity

r = Radius

Our values are given as

[tex]m = 0.4kg\\r = 0.75m\\F_c = 450N[/tex]

Rearranging to find the velocity we have that,

[tex]F_c = \frac{mv^2}{r}[/tex]

[tex]v = \sqrt{\frac{F_c * r}{m}}[/tex]

[tex]v = \sqrt{\frac{450 * 0.75}{0.4}}[/tex]

[tex]v = 29.0474m/s[/tex]

Therefore the  maximum speed can the mass have if the string is not to break is 29m/s

snehashish65

29.0474 m/s is the maximum speed.

What is the centripetal force explain?

A centripetal force is a force that makes a body follow a curved path.

In centripetal force, The force F necessary to keep a body in uniform circular motion.

The magnitude of the force is[tex]F_{e} = \frac{mv^{2} }{r}[/tex]

According to the question,

Given mass(m)=  0.4 kg

radius (r) = 0.75 m  and Force ([tex]F_{e}[/tex]) = 450N

[tex]F_{e} = \frac{mv^{2} }{r} \\v = \sqrt{\frac{F_{e}*r}{m} } = \sqrt{\frac{450*0.75}{0.4} } = 29.0474 m/s[/tex]

Therefore , 29.0474 m/s  is the maximum speed, if the string is not to break.

Learn more about centripetal force here :

https://brainly.com/question/11324711

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