A block of mass 1.6 kg is attached to a horizontal spring that has a force const

Question

A block of mass 1.6 kg is attached to a horizontal spring that has a force constant of 1.0 times 10^3 N/m, as shown in Figure 7.10. The spring is compressed 2.0 cm and is then released from rest, (a) Calculate the speed of the block as it passes through the equilibrium position x = 0 if the surface is frictionless. Calculate the speed of the block as it passes through the equilibrium position if a constant frictional force of 4.0 N retards its motion from the moment it is released. A 6.0-kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 12 N. a) Find the speed of the block after it has moved 3.0 m. Find the final speed of the block described in Example above if the surface is not frictionless but instead has a coefficient of kinetic friction of 0.15.

Explanation / Answer

a) using energy conservation,

initial spring PE + KE = final spring PE +KE = constant

springPe = kx^2 /2

KE = m v^2 /2

1000 * 0.02^2 /2 + 0 = 0 + 1.6v^2 /2

v = 0.5 m/s

b) now using work - energy theorem,

work done by spring + work done by friction = change in KE

1000(0.02^2 - 0)/2 - (4 * 0.02) = 1.6v^2/2 - 0

v = 0.39 m/s

2, a)

using work energy theorem,

work done by force = change in KE

3 * 12 = 6v^2/2 - 0

v = 3.46 m/s

b) now f = uk N = uk mg = 0.15 * 6* 9.8 = 8.82 N

work done by force + work done by friction = change in kE

3*12 - 3*8.82 = 6v^2/2 - 0

v = 1.78 m/s

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