HELP PLEASE 6. A massless spring (k = 275 N/m) k fixed to the left side of a lev

Question

HELP PLEASE

6. A massless spring (k = 275 N/m) k fixed to the left side of a level track. A block of mass 0.50 kg is pressed against the spring and compresses it a distance d, as shown. The block, initially at rest, k then released and travels toward a circular loop of radius R = 1.5 m. The entire track and the loop are frictionless, except for the section of the track between points A and B. Given that the coefficient of kinetic friction between the block and the section AB is 0.30 and the length of section AB is 2.5 m, determine the distance that the spring must be compressed from point A that will enable the block to just make it through the loop at point C. a. Use conservation of energy to find the kinetic energy at the bottom of the loop, point B b Use the work-kinetic energy theorem to find the kinetic energy at point & The kinetic energy at A is the kinetic energy at B plus the work done by friction as the block moves from A to B c. Use conservation of energy to find the distance that the spring is compressed

Explanation / Answer

a)

at the top of loop ,

mv^2/R = mg

v^2 = 9.8 * 1.5

v = 3.83 m/s

Now, at point P

KE = 0.5 * m*v^2 + mg*2R

KE = 0.50 * (0.5 * 3.83^2 + 9.8 * 2 * 1.5)

KE = 18.4 J

the kinetic energy at point B is 18.4 J

b)

Kinetic energy at A = 18.4 + 0.30 * 0.5 * 9.8 * 2.5

Kinetic energy at A = 22.1 J

the Kinetic energy at A is 22.1 J

c)

Now,

0.5 * k*x^2 = 22.1

0.5 * 275 *x^2 = 22.1

x = 0.4 m

the spring is compressed by 0.4 m

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