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a spring powered cannon, with spring constant k, is pointed straight into the air. it is loaded with a ball of mass m that is compressing the spring of the cannon a distance x and is ready to launch. write the equation to solve for the height of the ball after being launched and after it has reached it highest height and is now traveling down. do so in terms of k,m,x,v, and any needed constants.



Answer :

The height reached by the spring powered cannon is 9.8mh.

Calculation:-

PEspring = 1/2 × k × x²

Where k = spring constant

x = amount of compression

The spring constant is k

The compression of the spring is x = xm

The potential energy stored in the spring is

PE = 1/2 kx²

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of spring powered cannon

KEspring canon powered = 1/2 mu²

Let the height of the powered cannon be = h

The acceleration due to gravity is g = 9.8ms−2

Then ,

The potential energy of the spring powered cannon =  

PEpowered canon = mgh

Mass of the ball is m =m

PEcanon = m× h × 9.8

PEcanon = 9.8mh.

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