assuming the reference line to measure the height for gravitational potential energy lying at the equilibrium position
m = mass attached to the spring = 10.00 kg
k = spring constant of the spring = 250 N/m
h = height of the mass above the reference line or equilibrium position = 0.50 m
x = compression of the spring = 0.50 m
v = speed of mass = 2.4 m/s
A = maximum amplitude of the oscillation
v' = speed of mass at the maximum amplitude location = 0 m/s
using conservation of energy between the point where the speed is 2.4 m/s and the highest point at which displacement is maximum from equilibrium
kinetic energy + spring potential energy + gravitational potential energy = kinetic energy at maximum amplitude + spring potential energy at maximum amplitude + gravitational potential energy at maximum amplitude
(0.5) m v² + m g h + (0.5) k x² = (0.5) m v'² + m g A + (0.5) k A²
inserting the values
(0.5) (10) (2.4)² + (10) (9.8) (0.50) + (0.5) (250) (0.50)² = (0.5) (10) (0)² + (10) (9.8) A + (0.5) (250) A²
109.05 = (98) A + (125) A²
A = 0.62 m
Explanation:
Buoyancy force is equal to the weight of the displaced fluid:
B = ρVg
where ρ is the density of the fluid,
V is the volume of the displaced fluid,
and g is the acceleration due to gravity.
The fluid is water, so ρ = 1000 kg/m³.
The volume displaced is that of a sphere with radius 2 m:
V = 4/3 π r³
V = 4/3 π (2 m)³
V ≈ 33.5 m³
The buoyancy force is therefore:
B = (1000 kg/m³) (33.5 m³) (9.8 m/s²)
B ≈ 328,400 N
Round as needed.
Lab results:
Smoke detector = 40.0 cpm
Geiger counter
Americium-241 = 10,400 cpm
Geiger counter
The great difference in the radiation level means that
Americium-241 is more radioactive than the smoke detector itself. Americium-241
is used as a source of alpha radiation. This radiation ionizes the air
particles inside the smoke detector allowing it to conduct small amounts of
electric current. For example, if smoke particles go inside the smoke detector,
these are hit by alpha radiation and thus causing a drop in current. The drop
in current is detected by the smoke detector which then sets off the alarm.