Please answer just Question number 3 Thanks Show that If we have elastic collisi
ID: 1472365 • Letter: P
Question
Please answer just Question number 3 Thanks
Show that If we have elastic collision: r=m_A/m_B If m_B>>m_A: phi_A=theta If m_B=m_A: phi_A=theta/2 If we have inelastic collision prove (7.6.18): A particle of mass 4.0 kg has initial lunctic energy of 8.0 J and scratters elastically from tin 8.0 kg stationary particle. The original particle scatter by 30 degree. Find the final speeds and angles of the two particles. Repeat in the case of Q=2.0 J. A particle of mass m slides on a thin, circular hoop of radius R that spins about its axis (see the picture) with constant angular velocity omega. It can move only around the hoop. Write the equation of motion of the using Lagrange's equation in terms of the angle theta. Find the equilibrium position Find the frequency and the period of small oscillations about the equilibrium position found in b) and equation of motion from part a).Explanation / Answer
Mass of 1st Particle, m1 = 4.0 kg
Mass of 2nd Particle, m2 = 4.0 kg
Initial Kinetic Energy = 1/2 * mv1^2 = 8.0
v1 = sqrt(8.0 * 2 /4)
v1 = 2 m/s
Now Using Momentum Conservation -
In X direction -
v2 * cos(30 ) = v1 * cos()
v2 * cos(30 ) = 2 * cos()
v2 = 2/cos(30) * cos()
In Y direction -
v2 * sin(30) = v1 * sin()
v2 * sin(30) = 2 * sin()
Substituing Value of v2
(2/cos(30)) * sin(30)* cos() = 2 * sin()
2 * tan(30) = 2 * tan()
= 30.0
Therefore Angle = 30.0o
Speed = 2.0 m/s