Conservation of Momentum
Conservation of momentum can be applied when there is not a significant, net, external force on a system of objects. This is sometimes true (and therefore useful) for analyzing collisions, but not always! For which of the following collisions does conservation of momentum apply? Think about each one carefully.
Conservation of momentum can be applied when there is not a significant, net, external force on a system of objects. This is sometimes true (and therefore useful) for analyzing collisions, but not always! For which of the following collisions does conservation of momentum apply? Think about each one carefully.
A) A person gets punched in the face. The system consists of the fist of one person and the head of the other person.
A) A person gets punched in the face. The system consists of the fist of one person and the head of the other person.
B) A running back in a football game jumps into the air and is tackled by a linebacker (who has also jumped into the air). The system consists of the linebacker and the running back.
B) A running back in a football game jumps into the air and is tackled by a linebacker (who has also jumped into the air). The system consists of the linebacker and the running back.
C) A car hits a tree. The tree remains in place while the car comes to a stop. The system is the car and the tree.
C) A car hits a tree. The tree remains in place while the car comes to a stop. The system is the car and the tree.
D) A monster truck smashes into a Hyundai Excel. The system is the monster truck and the Hyundai.
D) A monster truck smashes into a Hyundai Excel. The system is the monster truck and the Hyundai.
E) Two ice skaters push one another apart while their skating blades remain parallel. The system is the two ice skaters.
E) Two ice skaters push one another apart while their skating blades remain parallel. The system is the two ice skaters.
F) A tennis racket hits a ball. The system is the tennis racket and the ball.
F) A tennis racket hits a ball. The system is the tennis racket and the ball.
G) A person uses a hammer to pound a nail into a wall. The system consists of the hammer and nail.
G) A person uses a hammer to pound a nail into a wall. The system consists of the hammer and nail.
H) A ball bounces off a floor. The system is the ball and the floor.
H) A ball bounces off a floor. The system is the ball and the floor.
I) Two astronauts in outer space play catch with a ball. The system is the two astronauts and the ball.
I) Two astronauts in outer space play catch with a ball. The system is the two astronauts and the ball.
J) Two lineman during a football game smash into one another. They have excellent traction with their cleated shoes.
J) Two lineman during a football game smash into one another. They have excellent traction with their cleated shoes.
Solution: B, D, E, and I.
Solution: B, D, E, and I.
For interaction A, the head has a significant external force exerted by the (presumably still attached) neck and the fist has a significant external force exerted by the arm. So momentum is not conserved for this system.
For interaction A, the head has a significant external force exerted by the (presumably still attached) neck and the fist has a significant external force exerted by the arm. So momentum is not conserved for this system.
For interaction B, there is an external force of weight (for both of them) in the y direction. But there are no significant net external forces in the x direction, so conservation of momentum can be used in that dimension.
For interaction B, there is an external force of weight (for both of them) in the y direction. But there are no significant net external forces in the x direction, so conservation of momentum can be used in that dimension.
For interaction C, the tree is attached by its roots to the ground which exerts a significant external force on the tree. So momentum is not conserved for this system. You can also look at the initial momentum which was not zero and compare it to the final momentum which is zero in order to reach the same conclusion.
For interaction C, the tree is attached by its roots to the ground which exerts a significant external force on the tree. So momentum is not conserved for this system. You can also look at the initial momentum which was not zero and compare it to the final momentum which is zero in order to reach the same conclusion.
For interaction D, there is an external force of friction, but this is likely to be small compared to the very large internal forces during the collision. So momentum is conserved for this system.
For interaction D, there is an external force of friction, but this is likely to be small compared to the very large internal forces during the collision. So momentum is conserved for this system.
For interaction E, there is an external force of friction, but this is likely to be small compared to the very large internal forces while the skaters push apart. So momentum is conserved for this system.
For interaction E, there is an external force of friction, but this is likely to be small compared to the very large internal forces while the skaters push apart. So momentum is conserved for this system.
For interaction F, the racket has a significant external force exerted by a hand. So momentum is not conserved for this system.
For interaction F, the racket has a significant external force exerted by a hand. So momentum is not conserved for this system.
For interaction G, the hammer has a significant external force by a hand and the nail has a significant external force of friction by the wall. So momentum is not conserved for this system.
For interaction G, the hammer has a significant external force by a hand and the nail has a significant external force of friction by the wall. So momentum is not conserved for this system.
For interaction H, the floor has a significant external force exerted upon it by the rest of the house (sub-floor). So momentum is not conserved for this system. Also, the momentum of the floor remains zero while the momentum of the ball changed (change of direction and possibly magnitude), so momentum is clearly not conserved for the system.
For interaction H, the floor has a significant external force exerted upon it by the rest of the house (sub-floor). So momentum is not conserved for this system. Also, the momentum of the floor remains zero while the momentum of the ball changed (change of direction and possibly magnitude), so momentum is clearly not conserved for the system.
For interaction I, there are no external forces on the system, so momentum is conserved.
For interaction I, there are no external forces on the system, so momentum is conserved.
For interaction J, there is significant friction from the ground onto the players, so momentum is not conserved.
For interaction J, there is significant friction from the ground onto the players, so momentum is not conserved.