to solve the question please use the equations below. - a mass M moving with a velocity V1i collides with mass 2M moving with a velocity V2i. After the collision the first mass has a velocity V1f.make a diagram of the initial momemtub vectors and final momentum vectors in a (x,y) plane.determine the final velocity of the second mass in (I J K) notation.determine the final velocity of the second mass in terms of speed and angle.V1i=12 i -5J V2i= -3i +2J V1f= 8i +7J **Physics Formulas and Concepts****Rotational Motion:**- \( \theta = s/r \)- \( \omega = v/r \)- \( \alpha = a_t/r \)- \( a_c = \omega^2r \)Equations of motion:- \( \omega = \omega_0 + \alpha t \)- \( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 \)- \( \omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0) \)**Conditions of Static Equilibrium:**- \( \Sigma F_x = 0 \)- \( \Sigma F_y = 0 \)- \( \Sigma T_{\text{cw}} = \Sigma T_{\text{ccw}} \)**Vibrational Motion:**- \( T = \frac{1}{f} \)- \( \omega = 2 \pi f \)- \( \omega = \sqrt{k/m} \)Displacement, velocity, and acceleration in SHM:- \( x(t) = A \cos (\omega t + \phi) \)- \( v(t) = -A \omega \sin (\omega t + \phi) \)- \( a(t) = -A \omega^2 \cos (\omega t + \phi) \)Max values:- \( v_{\text{max}} = A \omega \)- \( a_{\text{max}} = A \omega^2 \)- \( F_{\text{max}} = m A \omega^2 \)**Waves:**- \( v = f \lambda \)- \( v = \sqrt{T/\mu} \), \( \mu \) = mass/length- \( f_n = n f_0 \)- \( l_n = 2L/n \)**Calorimetry:**- \( q = mc \Delta T \) or \( q = \Delta H m \)**Ideal Gas Law:**- \( PV = nRT \)- \( R = 8.314 \, \text{L-kPa/mol-K} \)**Moment of Inertia:**- For a ring: \( I = MR^2 \)- For a disc: \( I = \ ### Physics Formulas and Concepts#### Angles and Vector Components- **180 degrees = π radians**- **Vector components:** - \( V_x = V \cos \theta \) - \( V_y = V \sin \theta \) - \( V_x^2 + V_y^2 = V^2 \) - \( \tan \theta = \frac{V_y}{V_x} \)#### Constant Acceleration Conditions- \( v = v_0 + at \)- \( d = d_0 + v_0 t + \frac{1}{2} at^2 \)- \( v^2 = v_0^2 + 2a(d-d_0) \)- **Use \( g = 10 \, \text{m/s}^2 \)**#### Newton's Second Law of Motion- \( \Sigma F = ma \)#### Forces and Energy- **Gravitational force, or weight:** \( F_g = mg \)- **Frictional force:** \( F_f = \mu N \)- **Hooke’s law:** \( F = -kx \)- **Centripetal force:** \( F_c = \frac{mv^2}{r} \)#### Conservation of Energy- \( \Sigma E_i + W = \Sigma E_f \)#### Work and Energy- **Work:** \( W = F \Delta d \cos \theta \)- **Gravitational potential energy:** \( U_g = mgh \)- **Spring potential energy:** \( U_s = \frac{1}{2} kx^2 \)- **Kinetic energy:** \( KE = \frac{1}{2} mv^2 \) or \( \frac{1}{2} I \omega^2 \)#### Impulse and Momentum- **Impulse:** \( J = F \Delta t \)- **Momentum:** \( p = mv \)- **Momentum conservation:** \( \Sigma p_i + J = \Sigma p_f \)#### Angular Motion- **Torque:** \( T = I \alpha = Fr \sin \theta \)- **Moment of inertia:** \( I = \Sigma mr^2 \)These equations are fundamental in understanding the principles of physics and are used to calculate various physical quantities.

Name: to solve the question please use the equations below. - a mass M movin
Uploaded: 2024-03-20T06:57:37.000Z
Channel: Bartleby
Description: to solve the question please use the equations below. - a mass M moving with a velocity V1i collides with mass 2M moving with a velocity V2i. After the collision the first mass has a velocity V1f.make a diagram of the initial momemtub vectors and fin