\( [5 \mathrm{marks}] \) QLFSTION? FICARRE2.2 FIGURE \( 2.2 \) shoms one cnd of a horizontal spring \( \left(k=80.0 \mathrm{~N} \mathrm{~m}^{-1}\right) \) is hek fiued while an exlcmul force is. appliod to the froe end, stretching it slowly from \( x-0 \) to \( x=400 \mathrm{~cm} \). (a) Calsulate the work done by the applied force on the spring. (b) Calculane the additional week done in stretching the spring firom \( x=4.004 \mathrm{~cm} \) to \( x=700 \mathrm{~cm} \). \( [5 \) marks \( ] \) Page 4 of 9
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(1I) A spring has $k = 65 \mathrm { N } / \mathrm { m }$ . Draw a graph like that in Fig. 11 and use it to determine the work needed to stretch the spring from $x = 3.0 \mathrm { cm }$ to $x = 6.5 \mathrm { cm } ,$ where $x = 0$ refers to the spring's unstretched length.
A spring has a force constant of $500.0 \mathrm{N} / \mathrm{m}$. Show that the potential energy stored in the spring is as follows: a. $0.400 \mathrm{J}$ when the spring is stretched $4.00 \mathrm{cm}$ from equilibrium b. 0.225 J when the spring is compressed $3.00 \mathrm{cm}^{-}$ from equilibrium c. zero when the spring is unstretched (See Sample Problem $5 \mathrm{D}$.)
A certain spring is found $n o t$ to conform to Hooke's law. The force (in newtons) it exerts when stretched a distance $x$ (in meters) is found to have magnitude $52.8 x+38.4 x^{2}$ in the direction opposing the stretch. (a) Compute the work required to stretch the spring from $x=0.500 \mathrm{~m}$ to $x=1.00 \mathrm{~m} .$ (b) With one end of the spring fixed, a particle of mass $2.17 \mathrm{~kg}$ is attached to the other end of the spring when it is stretched by an amount $x=1.00 \mathrm{~m} .$ If the particle is then released from rest, what is its speed at the instant the stretch in the spring is $x=0.500 \mathrm{~m} ?$ (c) Is the force exerted by the spring conservative or nonconservative? Explain.
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