The sky is blue because: Select one: a. the index of refraction for air is slightly larger for blue than for red b. atomic hydro
gen is blue c. air molecules tend to polarize light along a horizontal axis d. oxygen and nitrogen molecules are small compared to the wavelengths of visible light e. oxygen molecules have a lower energy ground state than nitrogen molecules
Since no friction present, assuming no external forces acting during the three collisions, total momentum must be conserved.
For the first collission, only mass 1 is moving before it, so we can write the following equation:
Since both masses are identical, and they stick together after the collision, we can express the final momentum as follows:
From (1) and (2) we get:
v₁ = v₀/2 (3)
Since the masses are moving on a frictionless 1D track, the speed of the set of mass 1 and 2 combined together before colliding with mass 3 is just v₁, so the initial momentum prior the second collision (p₁) can be expressed as follows:
Since after the collision the three masses stick together, we can express this final momentum (p₂) as follows:
From (4) and (5) we get:
v₂ = v₀/3 (6)
Since the masses are moving on a frictionless 1D track, the speed of the set of mass 1, 2 and 3 combined together before colliding with mass 4 is just v₂, so the initial momentum prior the third collision (p₂) can be expressed as follows:
Since after the collision the four masses stick together, we can express this final momentum (p₃) as follows:
From (7) and (8) we get:
v₃ = v₀/4
This means that after the last collision, the speed will have been reduced to a 25% of the initial value, so it will have been reduced in a 75% regarding the initial value of v₀.
This is the equation for elastic potential energy, where U is potential energy, x is the displacement of the end of the spring, and k is the spring constant. <span> U = (1/2)kx^2 </span><span> U = (1/2)(5.3)(3.62-2.60)^2 </span> U = <span>
<span>2.75706 </span></span>J