Two objects slide without friction on a circular ring of radius r oriented in a vertical plane. the heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. the fixed end of the spring is attached to a point a horizontal distance 2r from the center of the circle. the lighter object (of mass m) is initially at rest at the bottom of the ring. the heavier object is released from rest at the top of the ring, then collides with and sticks to the lighter object. find the value for m that will allow the combined object (of mass 4m) to just reach the point a on the ring, but go no higher. express your answer in terms of some or all of the quantities k, r and the acceleration of gravity g.

Ifound this on google i hope it you

Velocity is the speed of an object in a certain direction so you'd need to know speed and direction

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s