Answer:
spring compressed is 0.724 m
Explanation:
given data
mass = 1.80 kg
spring constant k = 2 × 10² N/m
initial height = 2.25 m
solution
we know from conservation of energy is
mg(h+x) = 0.5 × k × x² ...................1
here x is compression in spring
so put here value in equation 1 we get
1.8 × 9.8 × (2.25+x) = 0.5 × 2× 10² × x²
solve it we get
x = 0.724344
so spring compressed is 0.724 m
Answer:
a) α = 0.338 rad / s² b) θ = 21.9 rev
Explanation:
a) To solve this exercise we will use Newton's second law for rotational movement, that is, torque
τ = I α
fr r = I α
Now we write the translational Newton equation in the radial direction
N- F = 0
N = F
The friction force equation is
fr = μ N
fr = μ F
The moment of inertia of a saying is
I = ½ m r²
Let's replace in the torque equation
(μ F) r = (½ m r²) α
α = 2 μ F / (m r)
α = 2 0.2 24 / (86 0.33)
α = 0.338 rad / s²
b) let's use the relationship of rotational kinematics
w² = w₀² - 2 α θ
0 = w₀² - 2 α θ
θ = w₀² / 2 α
Let's reduce the angular velocity
w₀ = 92 rpm (2π rad / 1 rev) (1 min / 60s) = 9.634 rad / s
θ = 9.634 2 / (2 0.338)
θ = 137.3 rad
Let's reduce radians to revolutions
θ = 137.3 rad (1 rev / 2π rad)
θ = 21.9 rev
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