Answer:
a. 16 s b. -1.866 kJ
Explanation:
a. Since the initial rotational speed ω₀= 3313 rev/min = 3313/60 × 2π rad/s = 346.94 rad/s. Its rotational speed becomes ω₁ = 0.75ω₀ in time t = 4 s.
We find it rotational acceleration using α = (ω₁ - ω₀)/t = (0.75ω₀ - ω₀)/t = ω₀(0.75 - 1)/t = -0.25ω₀/t = (-0.25 × 346.94 rad/s)/4 s = -21.68 rad/s².
Since the turntable stops at ω = 0, the time it takes to stop is gotten from
ω = ω₀ + αt and t = (ω - ω₀)/α = (0 - 346.94 rad/s)/-21.68 rad/s² = (-346.94/-21.68) s = 16 s.
So it takes the turntable 16 s to stop.
b. The workdone by the turntable to stop W equals its rotational kinetic energy change.
So, W = 1/2Iω² - 1/2Iω₀² = 1/2 × 0.031 kgm² × 0² - 1/2 × 0.031 kgm² × (346.94 rad/s)² = 0 - 1865.7 J = -1865.7 J = -1.8657 kJ ≅ -1.866 kJ
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Answer:
Explanation:
Sun - - - - - Earth----Capital building----Human----Atom
The sun would exert more gravitational force because it is the massive.
Gravitational force is directly proportional to mass.
Answer:
122.2
Explanation:
From the question, the equation of the force acting on the crate is,
F-mg = ma
F = ma+mg ........................ Equation 1
Where F = upward force, m = mass of the crate, a = acceleration of the crate, g = acceleration due to gravity of the crate.
Given: m = 5.0 kg, g = 9.8 m/s²
And a,
a = d²y/dt²
Where,
y(t) = 2.8t+0.61t³
d²y/dt² = 3.66t................... equation 2
when t = 4.0 s.
substitute into equation 2
d²y/dt² = a = 3.66(4)
a = 14.64 m/s²
substitute into equation 1,
F = 5(14.64)+5(9.8)
F = 73.2+49
F = 122.2 N.
