Answer:
If x₁=12 cm then k=1.7985 N/m
If x₂=15 cm then k=1.4388 N/m
Explanation:
Hanging mass= 22 g=0.022 kg
Acceleration due to gravity g=9.81 m/s²
If x₁=displacement= 12 cm=0.12 m
k= spring constant
∴k = 1.7985 N/m
If x₂=15 cm=0.15 m
Force of the hanging mass is same however the spring constant will change
∴k = 1.4388 N/m
As the mass is not changing the spring constant has to change. That means that here there are two spring one with k=1.7985 N/m and the other with k= 1.4388 N/m
Answer:
The value is
Explanation:
From the question we are told
The pipe diameter at location 1 is
The velocity at location 1 is
The diameter at location 2 is
Generally the area at location 1 is
=>
=>
=>
Generally the area at location 1 is
=>
=>
Generally from continuity equation we have that
=>
=>
=>
Answer:
109656.25 Nm
Explanation:
= Final angular velocity = 1.5 rad/s
= Initial angular velocity = 0
= Angular acceleration
t = Time taken = 6 s
m = Mass of disk = 29000 kg
r = Radius = 5.5 m
Torque is given by
The torque specifications must be 109656.25 Nm
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