Asmall 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°.

42.49

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

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 = 9.81  / Tan(13.0°)

Va = 42.49

The vans acceleration need to be 42.49  to create an angle of 13° with the Van's Roof

a and b sometimes have a positive value

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.