03 Dynamics Flashcards
With reference to Newton’s laws of motion, explain why in a closed system consisting of two bodies, the sum of their momenta must remain constant when they collide.
Applying 3rd Law: When the two bodies collide, they exert equal forces in opposite directions on each other.
Applying 2nd Law: Since impulse is the product of force and time of collision, the change in momentum of each body will be equal in magnitude and opposite in direction. Hence there is no net change in their total momentum.
Newton’s First Law of Motion
In the absence of resultant external force acting on it, a body at rest will remain at rest and a body in motion will continue its motion at constant velocity.
Newton’s Second Law of Motion
The rate of change in the momentum of a body is proportional to the resultant external force that acts on it, and the change in momentum is in the direction of the force.
Newton’s Third Law of Motion
When a body A exerts a force on body B, B exerts a reaction force on A that is equal in magnitude and opposite in direction to the action force.
Principle of Conservation of Momentum
Words:
In a collision between two bodies, the total momentum of both bodies remains constant provided no external force is exerted
Equation:
m1u1 + m2u2 = m1v1 + m2v2
Solving elastic collisions
No energy is lost (as heat and/or sound) in the collision
1) CoM: m1u1 + m2u2 = m1v1 + m2v2
2a) Relative speed of approach = relative speed of separation
u2 − u1 = v1 − v2
2b) Conservation of Kinetic Energy
½m1u12 + ½m2u22 = ½m1v12 + ½m2v22
Solve for (1) & (2a)
or solve for (1) & (2b)
Solving inelastic collisions
Some energy is lost (as heat and/or sound) in the collision
1) CoM: m1u1 + m2u2 = m1v1 + m2v2
RSA=RSP and CoM cannot be applied here
Solve for (1)
Solving completely/perfectly inelastic collisions
Maximum energy is lost (as heat and/or sound) in the collision (not necessarily all energy)
1) CoM: m1u1 + m2u2 = m1v1 + m2v2
2) Same final velocity
v1 = v2
Solve for (1) & (2)
