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A 200g block on a 50cm long string swings in a circle, it's frictionless and 75rpm. What is its speed and tension on string

Sagot :

Jackattackbluntidn
angular velocity = (75x2pie)/60
                          =2.5pie ras^-1 
linear velocity(or speed) at end of string, v = radius x angular velocity
                                                           v= 0.5 x 2.5pie
                                                           v=3.93 ms^-1

tension of string (I beleve is centeral force aplied by string), F= (mv^2)/r
                                                                                      F= (0.2 x 3.93^2)/0.5
                                                                                      F=6.18 N
(sorry if wrong)
Carlosegoidn

The speed of the block is given by:

[tex] V = w * R
[/tex]

Where,

w: angular speed

r: radius of the circular path.

The angular velocity must be in radians over seconds:

[tex] w = (75) * (2\pi) * (\frac{1}{60})

w = 7.85
[/tex]

The radius must be in the subway:

[tex] R = (50) * (\frac{1}{100})

R = 0.5 m
[/tex]

Then, the speed is given by:

[tex] V = (7.85) * (0.5)

[/tex]

[tex] V = 3.925 \frac{m}{s}
[/tex]

The tension of the rope is the centripetal force.

By definition, the centripetal force is:

[tex] F = m * (\frac{V^2}{R})
[/tex]

Where,

m: mass of the block in kilograms

Substituting values:

[tex] F = 0.2 * (\frac{3.925 ^ 2}{0.5})

F = 6.2 N
[/tex]

Answer:

its speed and tension on string are:

[tex] V = 3.925 \frac{m}{s}

F = 6.2 N [/tex]

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