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A small sphere hangs from a string attached to the ceiling of a uniformly accelerating train car. It is observed that the string makes an angle of 37° with respect to the vertical. The magnitude of the acceleration a of the train car is most nearly?

Respuesta :

Manetho

Answer:

a=7.384 m/s^2

Explanation:

let T be the tension in the string, m= mass

and a= acceleration

from the FBD in the attachment we can write

Tcos37°= mg

Tsin37° =ma

dividing both the equations we get

tan37° =a/g

therefore a=g×tan37°

a= 9.81×0.7535 = 7.384 m/s^2

the  magnitude of the acceleration a of the train = 7.384 m/s^2

Ver imagen Manetho
onyebuchinnaji

The magnitude of the acceleration a of the train car is most nearly 7.385 m/s².

The given parameters;

  • angle of inclination of the string, θ = 37⁰

The vertical component of the tension on the string;

Tcosθ = mg

The horizontal component of the tension on the string;

Tsinθ = ma

The coefficient of kinetic friction on the small sphere is calculated as;

[tex]\mu_k = \frac{Tsin(\theta)}{Tcos(\theta)} = \frac{ma}{mg} \\\\\mu_k = tan(\theta) = \frac{a}{g} \\\\a = \mu_kg = tan(\theta) \times g\\\\a = tan(37) \times 9.8\\\\a = 7.385 \ m/s^2[/tex]

Thus, the magnitude of the acceleration a of the train car is most nearly 7.385 m/s².

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