Provided that the only forces acting between objects within a system are internal forces, the total momentum of all objects within the system is conserved. That is, the total momentum of the system of objects before the explosion is equal to the total momentum of all objects after the explosion. This is known as the law of conservation of momentum.
Getting your Trinity Audio player ready...
Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.
Explosions - Law Enforcement - help1
There are 18 questions in all. Only the graphic varies from question to question. Each question displays a Before Explosion and an After Explosion diagram of three situations. The mass of each cart and the post-explosion velocity is depicted in each diagram. You must tap on any situation that violates the law of conservation of momentum.
Version 1
Two spring-loaded carts are at rest on a low-friction track. The spring is released, pushing the carts away from each other. Three situations are shown. Identify any situation that violates the law of momentum conservation. NOTE: The bricks on top of the carts have the same mass as the cart. The arrows represent the velocity of the cart.
The Underlying Principle
Momentum is conserved if the total momentum of the system of two carts is the same Before Explosion as it is After Explosion. Before the explosion, the momentum is zero since neither cart is in motion. So the After Explosion momentum of the two carts must also be zero in order for total system momentum to be conserved. In order for the two moving carts to have a total momentum of zero, the momentum of the red cart must be equal to but in the oppositie direction of the momentum of the blue cart.
Interpretting the Diagram
The diagrams show a cart that may or may not be loaded with bricks. Each brick has the same mass as a cart. And so a cart with a brick on it has twice the mass as an unloaded cart. And a cart loaded with two bricks has three times the mass as an unloaded cart.
The diagrams also show velocity vectors for the two carts in the After Explosion diagram. The length of the arrow is proportional to the velocity. The arrow lengths are either 1-unit long, 2-units long, or 3-units long.
Calculating the Momentum of a Cart
Momentum is the product of mass and velocity. It might be helpful to call the cart a 1-kg cart. As such, a cart loaded with a brick has a mass of 2 kg and a cart loaded with two bricks has a mass of 3 kg. Such designations would allow you to work with simple numbers that are true to the situation. Similarly, the velocities are either 1-unit, 2-units, or 3-units. So it might also be helpful to refer to these as 1 m/s, 2 m/s, and 3 m/s. Doing so allows you to work with numbers and perform quick and simple calculations of momentum from the product of mass and velocity.
Calculating Total System Momentum
Once you have calculated the momentum of the red cart and the blue cart (see above section), it's time to see if the total momentum of the system is zero after the explosion. If the red cart's momentum is equal to the blue cart's momentum (but in the opposite direction), then the total momentum is zero.