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Mamont248 [21]
3 years ago
14

A 2.00 kg box slides on a rough, horizontal surface, hits a spring with a speed of 1.90 m/s and compresses it a distance of 10.0

cm before coming to rest. Determine the force constant (in N/m) of the spring, if the coefficient of kinetic friction between the block and the surface is μk = 0.660.
Physics
2 answers:
Alik [6]3 years ago
5 0

Answer:

463.2 N/m

Explanation:

mass of block, m = 2 kg

velocity of spring, v = 1.9 m/s

distance, r = 10 cm = 0.1 m

coefficient of friction, μ = 0.66

Let the spring constant is K.

friction force, f = μ mg = 0.66 x 2 x 9.8 = 12.94 N

Use work energy theorem

\frac{1}{2}mv^{2}=f \times r + \frac{1}{2}Kr^{2}

0.5 x 2 x 1.9 x 1.9 = 12.94 x 0.1 + 0.5 x K x 0.1 x 0.1

3.61 = 1.294 + 0.005 K

K = 463.2 N/m

Thus, the spring constant is 463.2 N/m.

oksian1 [2.3K]3 years ago
3 0

Answer:

Explanation:

Given

mass of box m=2\ kg

speed of box v=1.9\ m/s

distance moved by the box x=10\ cm

coefficient of kinetic friction \mu _k=0.66

Friction  force f_r=\mu_kN

f_r=0.66\times mg

f_r=0.66\times 2\times 9.8=12.936 \N

Kinetic Energy of box will be utilize to overcome friction and rest is stored in spring in the form of elastic potential energy

\frac{1}{2}mv^2=f_r\cdot x+\frac{1}{2}kx^2

\frac{1}{2}\times 2\times 1.9^2=12.936\times 0.1+\frac{1}{2}\times k\times (0.1)^2

3.61-1.2936=0.005\times k

k=463.28\ N/m

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