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andreyandreev [35.5K]
3 years ago
10

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 = 13.0°.
Physics
1 answer:
Paraphin [41]3 years ago
3 0

Answer: 42.49 m/s^{2}

Explanation:

To solve this, we need to keep in mind the following:

While the sphere hangs it is under the effect of gravity. It is creating a Angle of 90° taking the roof as a reference.

Gravity can be noted as a Acceleration Vector. The magnitud for Earth's Gravity is a constant: 9.81 m/s^{2}

The acceleration of the Van will affect the sphere also, but this accelaration will be on the X-axis and perpendicular to the gravity. Because this two vectors are taking action under the sphere they will create a angle. This angle can be measured as a relation of the two magnitudes.

Tangent (∅) = Opossite Side / Adyacent Side

By trigonometry, we know the previous formula. This formula allows us to find the Tangent of a angle as a relation between the two perpendiculars magnitudes. In this case the Opossite Side will be the Gravity Accelaration, while the Adyancent Side is the Van's Acceleration.

(1)  Tangent (∅) = Gravity's Acceleration (G) / Van's Acceleration (Va)        

Searching for the Va in (1)

Va = G/Tan(∅)

Where ∅ in this case is equal to 13.0°

Va = 9.81m/s^{2}  / Tan(13.0°)

Va = 42.49 m/s^{2}

The vans acceleration need to be 42.49 m/s^{2}  to create an angle of 13° with the Van's Roof

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