Respuesta :
Answer:
1) The disc speed of 0.450 kg is vif = -2.0 m / s
2) The disc is receding because the negative bone velocity is heading west
3) Disc speed 0.950 kg V2f = 3.6 m / s
4) The disk follows the initial direction of the light disk, bone moves east
Explanation:
For the problems of crashes we have to define a system in this case the system is formed by the two disks, write the amount of movement before and after the crash
p₀ = m₁ v₁₀ + 0
pf = m₁ v₁f + m₂ v₂f
For the system during the crash all forces are internal, so the moment is preserved
po = pf
m₁ v₁₀ = m₁ v₁f + m₂ v₂f
Like elastic shock, kinetic energy is also conserved
Ko = Kf
½ m₁ v₁₀² = ½ m₁ v₁f² + ½ m₂ v₂f²
Let's write the system of equations
m₁ (v₁₀ -v₁f) = m₂ v₂f
m₁ (v₁₀² - v₁f²) = m₂ v₂f²
We replace the first in the second
m₁ (v₁₀² - v₁f²) = m₂ [m₁ (v₁₀ -v₁f) / m₂]²
m₁ (v₁₀² - v₁f²) = [m1² (v₁₀ -v₁f)² / m₂
(v₁₀² - v₁f²) = [m₁ (v₁₀ -v₁f)² / m₂
m₁ (v₁₀ - v₁f) (v₁₀ + v₁f) = [(v₁₀ -v₁f)² m₁ / m₂
(v₁₀ + v₁f) = (v₁₀ -v₁f) m₁ / m₂
v₁f (1+ m₁ / m₂) = v₁₀ (m₁ / m₂ -1)
v₁f (m₂ + m₁) / m₂ = v₁₀ (m₁ -m₂) / m₂
v₁f = v₁₀ [(m₁ -m₂) / (m₁ +m₂)]
We calculate
V₁f = 5.6 [(0.450 -0.950) / ((0.450+ 0.90)] = 5.6 (-0.500 /1.4)
V₁f = - 2.0 m / s
The negative sign indicates that the disk goes back
m₁ (v₁₀ -v₁f) = m₂ v₂f
v₂f = m₁ / m₂ (v₁₀ -v₁f)
v₂f = 0.450 / 0.950 (5.6 - (-2))
v₂f = 3.6 m / s
Let's write the results
1) The disc speed of 0.450 kg is vif = -2.0 m / s
2) The disc is receding because the negative bone velocity is heading west
3) Disc speed 0.950 kg V2f = 3.6 m / s
4) The disk follows the initial direction of the light disk, bone moves east
