If a 4.5 kg object is dropped from a height of 6.0 m, what will be its velocity when it is halfway toward the ground? (Use g = 9
2 answers:
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Answer:
a) v = 0.7071 v₀, b) v= v₀, c) v = 0.577 v₀, d) v = 1.41 v₀, e) v = 0.447 v₀
Explanation:
The speed of a wave along an eta string given by the expression
v =
where T is the tension of the string and μ is linear density
a) the mass of the cable is double
m = 2m₀
let's find the new linear density
μ = m / l
iinitial density
μ₀ = m₀ / l
final density
μ = 2m₀ / lo
μ = 2 μ₀
we substitute in the equation for the velocity
initial v₀ =
with the new dough
v =
v = 1 /√2 \sqrt{ \frac{T_o}{ \mu_o} }
v = 1 /√2 v₀
v = 0.7071 v₀
b) we double the length of the cable
If the cable also increases its mass, the relationship is maintained
μ = μ₀
in this case the speed does not change
c) the cable l = l₀ and m = 3m₀
we look for the density
μ = 3m₀ / l₀
μ = 3 m₀/l₀
μ = 3 μ₀
v =
v = 1 /√3 v₀
v = 0.577 v₀
d) l = 2l₀
μ = m₀ / 2l₀
μ = μ₀/ 2
v =
v = √2 v₀
v = 1.41 v₀
e) m = 10m₀ and l = 2l₀
we look for the density
μ = 10 m₀/2l₀
μ = 5 μ₀
we look for speed
v =
v = 1 /√5 v₀
v = 0.447 v₀
Answer:
b. Jupiter’s greater gravity has compressed the layers, so they are closer together there.
Explanation:
The value for Jupiter mass is 1.8981×10²⁷kg, while the mass of Saturn is 5.6832×10²⁶kg, so the different layers of clouds in Jupiter will be submitted to a greater gravitational pull because it has a bigger mass, as is established in the law of universal gravitation:
(1)
Where m1 and m2 are the masses of two objects, G is the gravitational constant and r is the distance between the two objects.
As it can be seen in equation 1, the gravitational force is directly proportional to the product of the masses of the objects, so if the mass increase the gravitational force will do it too.
For the case of Saturn, it has a lower mass so its layers of clouds will suffer a weaker gravitational pull. That leads to the three clouds being more spacing that the ones of Jupiter.