In a mattress test, you drop a 7.0 kg bowling ball from a height of 1.5 m onto a mattress
which, as a result, compresses 15 cm when the ball stops. (a) What is the kinetic energy of the ball before it hits
the mattress? (b) How much work does the gravitational force of the earth do on the ball when it falls in 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 does on the ball while it is compressing the mattress? (d) What is the force of interaction between
the mattress and the ball? Does it make sense to determine it from Newton's 2nd law to determine the work done
by it? Explain. (e) How much work does the mattress do on the ball? Now model the mattress as a single spring
with an unknown spring constant k and consider the entire system consisting of the ball, the ground, and the mattress. (f)
By how much does the potential energy of the mattress increase as it compresses? (g) What is the value of the spring constant
of the spring constant k?
answer only letters d,e,f,g
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