Spring double compression word problem. If a spring is pushed in on both sides, then both objects were realesed what would their velocity be?A toy has two cars of mass 50 g separated by a spring....

Spring double compression word problem. If a spring is pushed in on both sides, then both objects were realesed what would their velocity be?

A toy has two cars of mass 50 g separated by a spring. The spring constant is 800 N/m. If the spring is compressed by 1.5 cm and both cars are at rest, determine the speed the cars will have when the spring is released and the cars are free to move.

I know that you have to half x. But I dont understand why.

Asked on by lalalesli

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bandmanjoe's profile pic

bandmanjoe | Middle School Teacher | (Level 2) Senior Educator

Posted on

This is a question about elastic energy, which is the energy created by either stretching something or compressing something and storing potential energy into it.  If all things are equal, such as the mass of the two cars on either side of the spring, the amount of velocity created by both cars should be the same.  You would divide the velocity originally created by one-half because two cars were involved.  This would bring into play Newtons third law of motion, which basically states "For every action force, there is an equal and opposite reaction force".  So the force generated is distributed over two cars, which would mean you would need to divide the velocity by two, or halve it.  Think of it this way, if there were only one car involved, and the spring were pushing against a fixed point, all the velocity created would be exerted on the one car.  But since you have the velocity created distributed over two cars, each car receives half the force, resulting in half the velocity.

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