If a ball is accelerating down through the air with no horizontal motion, what must be true about the net forces acting on the b
1 answer:
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Answer:
v =
the speed in the two planes will be the same since it does not depend on the angle of the same
Explanation:
In this exercise we are told that the two inclined planes have no friction force, so we can apply the conservation of energy for each one, we will assume that the initial height in the two planes is the same
starting point. Highest part of each plane
Em₀ = U = m g h
final point. Lowest part of each plane
= K = ½ m v²
as there is no friction, the mechanical energy is preserved
Em₀ = Em_{f}
mg h = ½ m v²
v =
As we can see, the speed in the two planes will be the same since it does not depend on the angle of the same
Answer:
Ring v² = gh
solid wheel (cylinder) v² = 4/3 gh
Explanation:
Let's use conservation of energy to find the speed of the wheels at the bottom of the hill.
starting point. Point before starting movement
Em₀ = mgh
final point. At the bottom of the hill
Em_f = K = ½ m v² + ½ I w²
energy is conserved
Emo = Em_f
mgh = ½ m v² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
mgh = ½ m v² + ½ I v² / r²
mgh = ½ (m + I / r²) v²
v² =
the moments of inertia are tabulated
Ring
I = mr²
v² = 2 m g h / (m + m)
v² = gh
solid wheel (cylinder)
I = ½ m r²
v² = 2m gh / (m + m / 2)
v² = 4/3 gh
We can see that due to the difference in the moment of inertia of each body it is different, the solid wheel has more speed when it reaches the lower part of the ramp