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A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of θ with respect to the vertical. Find the acceleration of the van when θ = 12.8°.

Respuesta :

Answer:

[tex]a = 2.23 m/s^2[/tex]

Explanation:

As the small sphere is suspended by the string then the force due to tension is given as

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

[tex]T sin\theta = ma[/tex]

now we will have

[tex]tan\theta = \frac{ma}{mg}[/tex]

here we will have

[tex]a = g tan\theta[/tex]

here we know that

[tex]\theta = 12.8^o[/tex]

so we will have

[tex]a = (9.81)tan12.8[/tex]

[tex]a = 2.23 m/s^2[/tex]