1. This problem will use the general energy conservation principle discussed in
ID: 1884386 • Letter: 1
Question
1. This problem will use the general energy conservation principle discussed in class. Consider two blocks colliding inelastically and sticking on a level, frictionless surface. Block A (of mass m) is initially moving with velocity v. Block B (of mass M) is initially stationary of stiffness k absorbs the impact of their collision but does not recoil because of the ratchet. a) Find the internal energy change AU for this process. If all of this energy change is stored as the potential energy of the spring, find its displacement (i.e. extent of compression) A, which should be a combination of v, m and k. c) Now let's say that at the time of their collision, the surface is hotter (and much more massive than then blocks). Shortly after the collision, the blocks come up to the surface temperature. Find U a few seconds after the collision.Explanation / Answer
1. two blocks, colliding inelastically and sticking on level frictionless surface
mass A = m, velocity = v
mass B = M, stationary
spring stiffness = k
a. from conservation of meomentum
mv = (m + M)V
V = mv/(m + M)
hernce loss of KE = 0.5(M + m)V^2 - 0.5*m*v^2
dU = dKE = m^2v^2/2(m + M) - mv^2/2 = m(m/(m + M) - 1)v^2/2
b. 0.5k*x^2 = dU
x = sqrt(m(m/(m + M) - 1)/k)*v
c. so if the initially the surface temperature of the4 block is high and gradually blocks come to original temperatue
hence this means that increasing temeprature in the surface will now be usied as KE and hecne final KE of the system is more in this case
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