Chapter 08, Problem 055 In the figure, a block of mass m = 1.6 kg slides head on

Question

Chapter 08, Problem 055 In the figure, a block of mass m = 1.6 kg slides head on into a spring of spring constant k = 370 N/m, when the block stops, it has compressed the spring by 7.0 cm. The coefficient of kinetic friction between block and floor is 0.33. While the block is in contact with the spring and being brought to rest, what are (a) the work done by the spring force and (b) the increase in thermal energy of the block-floor system? (c) What is the block's speed just as the block reaches the spring? (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

a) Work by spring = -1/2*k*x^2 (It is negative because it opposes the motion)

W = -1/2*370N/m*(0.07m)^2 = -0.9065J

b) Increase in Thermal energy = -W by friction = µ*m*g*d = 0.33*1.6kg*9.8m/s^2*0.07m = 0.362J

c) Since W = K

We have Ki = -W= -(-0.9065 - 0.362) = 1.269J

So from K = 1/2*m*v^2 we have v = sqrt(2*K/m) = sqrt(2*1.269/1.6) = 1.586m/s

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