878) Answers are a) 0.100 m (quadratic) b) 0.0855 m I posted this question sever
ID: 1448192 • Letter: 8
Question
878) Answers are
a) 0.100 m (quadratic)
b) 0.0855 m
I posted this question several times but haven't received the correct answers.
878 A 2 kg block is dropped from a height of 40 cm onto a spring whose force constant, k, is 1960 N/m. What is the maximum distance the spring will be compressed, (a) (b) if we make the (unreasonable) assumption that no heat is lost when the block hits the spring? if we make the (reasonable) assumption that 30% of the block's kinetic energy, just before it hits the spring, is lost as heat?Explanation / Answer
(a) Consider the minimum energy level (for gravitational potential energy) that level corresponding to the maximum compression of the spring. At that point Epg=0, Ek=0. But at this point the elastic potential energy is maximum (kx2/2).
From that point up, we have at height h: Ei=mg(h+x)
x=maximum compression of the spring
h=0.4 m
Total energy conservation law between initial and final levels is written as: mg(h+x)=kx2/2
Replace the numbers, make the calculation (solve the eq) and get x=0.1m.
b) We need to find the kinetic energy at the level just before the block hits the spring.
Initially: mg(h+x).
At the level before the block hits the spring: mgx+mv2/2
Equal the last 2 eqs and get: mgh=mv2/2=7.84 J
30% from this value is: Eh=2.352 J.
The conservation energy becomes here the variation energy theorem, written as:
mg(h+x)-kx2/2=Eh
Replace the numbers, order the eq, solve it and get: x=0.0855 m.
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