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4 years ago

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A horizontal spring with spring constant 110 N/m is compressed 16 cm and used to launch a 2.7 kg box across a frictionless, hori

zontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Use work and energy to find how far the box slidesacross the rough surface before stopping.

1 answer:

qaws [65]4 years ago

7 0

Answer:

0.35 m

Explanation:

We are given that

Spring constant, $k=110N/m$

Length,l=16 cm= $16\times 10^{-2} m$

1 m=100 cm

Mass,m=2.7 kg

Coefficient of kinetic friction, $\mu_k=0.15$

Initial potential energy, $U_1=$ 0

Final potential energy, $K_2=0$

According to law of conservation of energy

$K_1+U_1=K_2+U_2$

$\frac{1}{2}kx^2=\mu mg d$

$d=\frac{kx^2}{\mu mg}=\frac{110\times (16\times 10^{-2})^2}{2\times 0.15\times 2.7\times 9.8}$

$d=0.35 m$

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