A 230 g block is dropped onto a vertical spring with force constant k = 3.0 N/cm

Question

A 230 g block is dropped onto a vertical spring with force constant k = 3.0 N/cm (Fig. 11-36). The block sticks to the spring, and the spring compresses 11 cm before coming momentarily to rest. (Ignore friction.)

(b) While the spring is being compressed, how much work is done by the spring?

My work:

(c) What is the speed of the block just before it hits the spring?

My work:

(d) If the speed at impact is doubled, what is the maximum compression of the spring?

My work:

Did quadratic formula to find y... and I got y = -.19593...m = 0.200m but I was told it is incorrect.

Explanation / Answer

Given that

mass m=0.230 kg

spring constant K=300 N/m

compression x=0.11 m

now we find the work done

work done W=1/2kx^2=1/2*300*0.11^2=1.815 J

now we find the speed

speed V=x[k/m]^1/2=0.11[300 / 0.230]^1/2=3.973 m/s

now we find the maximum compresson at speed is doubled

V1/V2=X1/X2

3.973/2*3.973=0.11/X2

the maximum compression X2=0.22 m

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