greg has a hoop and a solid cylinder, and wants to spin each around its axis of rotation. they have the same mass and radius. wh
1 answer:
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Answer: 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
Answer:
W = 290.7 dynes*cm
Explanation:
d = 1/5 cm = 0.2 cm
The force is in function of the depth x:
F(x) = 1000 * (1 + 2*x)^2
We can expand that as:
F(x) = 1000 * (1 + 4*x + 4x^2)
F(x) = 1000 + 4000*x + 4000*x^2
Work is defined as
W = F * d
Since we have non constant force we integrate
W = [1000*x + 2000*x^2 + 1333*X^3] evaluated between 0 and 0.2
W = 1000*0.2 + 2000*0.2^2 + 1333*0.2^3 - 1000*0 - 2000*0^2 - 1333*0^3
W = 200 + 80 + 10.7 = 290.7 dynes*cm