A block of mass 0.528 kg slides with uniform velocity of 3.60 m/s on a horizontal...
A block of mass 0.528 kg slides with uniform velocity of 3.60 m/s on a horizontal frictionless surface. At some point, it strikes a horizontal spring in equilibrium. If the spring constant is k = 26.1 N/m, by how much will the spring be compressed by the time the block comes to rest?
b. What is the amount of compression if the surface is rough under the spring, with coefficient of kinetic friction µk = 0.411?
Homework Answers
Using the energy equation
K.E + Wother = P.E
Where Wother = work done by other forces
1/2 mv2 - fk x = 1/2 kx2..............(1)
fk = ?kN=?k(mg)
1/2(0.528 kg )(3.60m/s)2 - (0.411)(0.528 kg)(9.80m/s2) x =1/2(26.1 N/m,)(x2)
Simplifying and arranging, we get
13.05 x2 + 2.1267 x - 3.42 = 0
x = 0.437 m
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