Answer:
Explanation:
The velocity v₁ can be calculated with the kinematic formula:
Since the object is initially at rest, v₁ becomes:
Where g is the acceleration due to gravity. Now, the velocity v₂ can be calculated with the same formula, but now the initial velocity is v₁:
Substituting v₁ in this expression and solving for v₂, we get:
Now, dividing v₂ over v₁, we get the expression:
It means that v₂ is √2 times v₁.
Answer:
5) 13 revolutions (approximately)
Explanation:
We apply the equations of circular motion uniformly accelerated :
ωf²= ω₀² + 2α*θ Formula (1)
Where:
θ : angle that the body has rotated in a given time interval (rad)
α : angular acceleration (rad/s²)
ω₀ : initial angular speed ( rad/s)
ωf : final angular speed ( rad/s)
Data:
ω₀ = 18 rad/s
ωf = 0
α = -2 rad/s² ; (-) indicates that the wheel is slowing
Revolutions calculation that turns the wheel until it stops
We apply the formula (1)
ωf²= ω₀² + 2α*θ
0 = (18)² + 2( -2)*θ
4*θ = (18)²
θ = (18)²/4 = 81 rad
1 revolution = 2π rad
θ = 81 rad * 1 revolution / 2πrad
θ = 13 revolutions approximately
