Question: i need a step by step on how to solve, i need to undestand what is going on to solve it, explanation if possible 7.8

i need a step by step on how to solve, i need to undestand what is going on to solve it, explanation if possible

7.8 Problems Problem 1 In a mattress test, you drop a 7.0 kg bowling ball from a height of 1.5m above a mattress, which as a result compresses 15 cm as the ball comes to a stop. (a) What is the kinetic energy of the ball just before it hits the mattress? (b) How much work does the gravitational force of the earth do on the ball as it falls, for the first part of the fall (from the moment you drop it to just before it hits the mattress)? (c) How much work does the gravitational force do on the ball while it is compressing the mattress? (d) How much work does the mattress do on the ball? (e) Now model the mattress as a single spring with an unknown spring constant k, and consider the whole system formed by the ball, the earth and the mattress. By how much does the potential energy of the mattress increase as it compresses? (f) What is the value of the spring constant k? ring of spring constant

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