Conservation of Linear Collision
Experiment 4
Inelastic Collisions, Conservation of Momentum and Non
Conservation of Kinetic Energy
Preparation
Prepare for this week's experiment by studying Newton's Laws, linear momentum, and kinetic energy. Principles
In this experiment you will study a collision where a moving object strikes and sticks to an initially motionless object. When the colliding objects stick together the collision is said to be completely inelastic. The net momentum of the system should not change, but the net kinetic energy of the system will decrease. The amount of kinetic energy left after the collision can be predicted using conservation of momentum.
Linear momentum is defined as
p = mv .
It is a vector quantity; the momentum is always in the same direction as the linear velocity. As long as the mass is constant, the time derivative of momentum is
dp dv =m . dt dt
Since the time derivative of the velocity is the acceleration, we see that
dp dv =m
= ma = ∑ F . dt dt
Force changes momentum. If no net force is applied to an object its momentum remains constant. Consider a collision between object 1 and object 2. If there is no other force on object 1 other than the force from object 2, or if the other forces on object 1 add to zero, then
dp1
= ma1 = ∑ F1 = F21 . dt The force from object 2 is the only thing changing the momentum of object 1.
If there is no other force on object 2 other than the force from object 1, or if the other forces on object 2 add to zero, then
dp2
= ma2 = ∑ F2 = F12 . dt 1
And similarly, the force from object 1 is the only thing changing the momentum of object 2.
Newton's Third Law states that if an object exerts a force on another object, the second object exerts an equal and opposite force on the first. So the force object 1 exerts on object 2, F12 , is equal and opposite to the force object 2 exerts on object 1, F21 . So we can write Newton’s Third
Law as
F12 = -F21 or as
F12 + F21 = 0 .
Using
Inelastic Collisions, Conservation of Momentum and Non
Conservation of Kinetic Energy
Preparation
Prepare for this week's experiment by studying Newton's Laws, linear momentum, and kinetic energy. Principles
In this experiment you will study a collision where a moving object strikes and sticks to an initially motionless object. When the colliding objects stick together the collision is said to be completely inelastic. The net momentum of the system should not change, but the net kinetic energy of the system will decrease. The amount of kinetic energy left after the collision can be predicted using conservation of momentum.
Linear momentum is defined as
p = mv .
It is a vector quantity; the momentum is always in the same direction as the linear velocity. As long as the mass is constant, the time derivative of momentum is
dp dv =m . dt dt
Since the time derivative of the velocity is the acceleration, we see that
dp dv =m
= ma = ∑ F . dt dt
Force changes momentum. If no net force is applied to an object its momentum remains constant. Consider a collision between object 1 and object 2. If there is no other force on object 1 other than the force from object 2, or if the other forces on object 1 add to zero, then
dp1
= ma1 = ∑ F1 = F21 . dt The force from object 2 is the only thing changing the momentum of object 1.
If there is no other force on object 2 other than the force from object 1, or if the other forces on object 2 add to zero, then
dp2
= ma2 = ∑ F2 = F12 . dt 1
And similarly, the force from object 1 is the only thing changing the momentum of object 2.
Newton's Third Law states that if an object exerts a force on another object, the second object exerts an equal and opposite force on the first. So the force object 1 exerts on object 2, F12 , is equal and opposite to the force object 2 exerts on object 1, F21 . So we can write Newton’s Third
Law as
F12 = -F21 or as
F12 + F21 = 0 .
Using