Answer:
The work done to get you safely away from the test is 2.47 X 10⁴ J.
Explanation:
Given;
length of the rope, L = 70 ft
mass per unit length of the rope, μ = 2 lb/ft
your mass, W = 120 lbs
mass of the 70 ft rope = 2 lb/ft x 70 ft
= 140 lbs.
Total mass to be pulled to the helicopter, M = 120 lbs + 140 lbs
= 260 lbs
The work done is calculated from work-energy theorem as follows;
W = Mgh
where;
g is acceleration due gravity = 32.17 ft/s²
h is height the total mass is raised = length of the rope = 70 ft
W = 260 Lb x 32.17 ft/s² x 70 ft
W = 585494 lb.ft²/s²
1 lb.ft²/s² = 0.0421 J
W = 585494 lb.ft²/s² = 2.47 X 10⁴ J.
Therefore, the work done to get you safely away from the test is 2.47 X 10⁴ J.
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
Answer:
Explanation:
Intensity of sound = sound energy emitted by source / 4 π d² , where d is distance of the source .
A )
Intensity of sound at 1 m distance = 60 /4 π d²
d = 1 m
Intensity of sound at 1 m distance = 60 /(4 π 1²)
= 4.78 W m⁻² s⁻¹
B )
Intensity of sound at 1.5 m distance = 60 /4 π d²
d = 1.5 m
Intensity of sound at 1 m distance = 60 /(4 π 1.5²)
= 2.12 W m⁻² s⁻¹
C )
Intensity of sound due to 4 speakers at 1.5 m distance = 4 x 60 /4 π d²
d = 1.5 m
= 4 x 60 /(4 π 1.5²)
= 8.48 W m⁻² s⁻¹
D )
Intensity of sound due to .06 W speaker must be 10⁻¹² W s ⁻² . Let the distance be d .
.06 /4 π d² = 10⁻¹²
d² = .06 /4 π 10⁻¹²
d = 6.9 x 10⁴ m .
You first need to convert the hours into minutes, then use the speed equals distance over time formula.
Answer:
Explanation:
Particles of a solid are closely packed, and when a solid is hit to produce a sound the kinetic energy present in the solid will cause the particles to vibrate vigorously in the intermolecular spaces in the solid, whereas the paticles of liquids and gases are rather further apart therefore having large intermolecular spaces between particles.