1) Block 1 with mass m, rests on a frictionless surface and is attached to a mj
ID: 1782988 • Letter: 1
Question
1) Block 1 with mass m, rests on a frictionless surface and is attached to a mj spring with spring constant k, and to a massless string going over a frictionless pulley to Block 2 which has mass m2. a) What is the extension x, of the spring if the system is at equilibrium (with the masses stationary)? b) Block 1 is held so the spring is at its relaxed length, then it is released. What is the maximum extension x2 of the spring before the masses come to a stop? i) Find the ratio of the extension in part b) to the extension in part a), xlx Find the extension x, of the spring when the kinetic energy of the two blocks is maximum. (Use your conservation of energy equation. You will need to take its time derivative and set it to zero. Note that both x and v are functions of time so both have time derivatives! Hint: what is the acceleration when K is maximum?). i) Find the ratio of x, to x ii) Find the kinetic energy of the system at this instant. c)Explanation / Answer
a] tension T = m2g
kx1 = m2g
x1 = m2 *g/k
b] By conservation of energy,
m2 g x2 = 0.5kx2^2
m2g = 0.5 kx2
x2 = 2*m2g/k
i) x2/x1 = 2
c] Kinetic energy will be maximum when a will be zero or net force will be zero.
x3 = x1 = m2g/k
i] x3/x1 = 1
ii] KE = change in potential energy
= m2gx3 - 0.5kx3^2
= m2g*m2g/k - 0.5*k*(m2g/k)^2
= 0.5 (m2g)^2/k
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