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A 5.49 kg ball is attached to the top of a vertical pole with a 2.15 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.654.65 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole. Take ????=9.81g=9.81 m/s2. angle: °

Respuesta :

Answer:[tex]\theta =45.73^{\circ}[/tex]

Explanation:

Given

Length of string =2.15 m

mass of ball =5.49 kg

speed of ball=4.65 m/s

Here

Tension provides centripetal acceleration

[tex]T\cos\theta =mg[/tex]-----1

[tex]T\sin \theta =\frac{mv^2}{r}[/tex]------2

Divide 2 & 1

[tex]tan\theta =\frac{v^2}{rg}[/tex]

[tex]tan\theta =\frac{4.65^2}{2.15\times 9.8}[/tex]

[tex]tan\theta =1.026[/tex]

[tex]\theta =45.73^{\circ}[/tex]

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