A massless spring of constant k = 77.0 N/m is fixed on the left side of a level
ID: 2252961 • Letter: A
Question
A massless spring of constant k = 77.0 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance of d. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is
A massless spring of constant k = 77.0 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance of d. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is mu k = 0.28, and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. [Hint: The force of the track on the block will be zero if the block barely makes it through the-loop-the-loop.Explanation / Answer
energy dissipated in the region AB is mu*m*g*d=3.43J
energy stored in spring = 0.5 *k*x^2 = 0.5 m*(vb)^2 + energy dissipated in region AB -(1)
where vb is the velocity of the block at the bottom of the loop
vb>=sqrt( 5*g*r) for completing the circle vetically
NOTE: velocity at the top of the loop is atleast sqrt(g*r) so that the centrifugal force balances mg and the block doesnt lose contact
from ---(1) : 0.5 kx^2 >= 0.5* m * 5*g*r + 3.43
so x = 0.75 metres
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