Answer:
(a) 1.85 m/s
(b) 4.1 m/s
Explanation:
Data
- initial bullet velocity, Vbi = 837 m/s
- wooden block mass, Mw = 820 g
- initial wooden block velocity, Vwi = 0 m/s
- final bullet velocity, Vbf = 467 m/s
(a) From the conservation of momentum:
Mb*Vbi + Mw*Vwi = Mb*Vbf + Mw*Vwf
Mb*(Vbi - Vbf)/Mw = Vwf
4.1*(837 - 467)/820 = Vwf
Vwf = 1.85 m/s
(b) The speed of the center of mass speed is calculated as follows:
V = Mb/(Mb + Mw) * Vbi
V = 4.1/(4.1 + 820) * 837
V = 4.1 m/s
The behavior of an ideal gas at constant temperature obeys Boyle's Law of
p*V = constant
where
p = pressure
V = volume.
Given:
State 1:
p₁ = 10⁵ N/m² (Pa)
V₁ = 2 m³
State 2:
V₂ = 1 m³
Therefore the pressure at state 2 is given by
p₂V₂ = p₁V₁
or
p₂ = (V₁/V₂) p₁
= 2 x 10⁵ Pa
Answer: 2 x 10⁵ N/m² or 2 atm.
The concept to develop this problem is the Law of Malus. Which describes what happens with the light intensity once it passes through a polarized material.
Mathematically this can be expressed as
Where
I = New intensity after pass through the Polarizer
= Original intensity
= Indicates the angle between the axis of the analyzer and the polarization axis of the incident light.
When the light passes perpendicularly through the first polarizer, the light intensity is reduced by half which will cause the intensity to be 
at the output of the new polarizer, mathematically:
Solving to find the angle we have
The orientation angle of the second polarizer relative to the first one is 43.11°
Mass is an intrinsic property of the rock. The mass doesn't care where it is, and it makes no difference where the rock happens to be at the moment ... its mass doesn't change.
17kg of mass is 17kg . If it's 17kg on the moon, it's <em>17kg</em> on Earth.
