A horizontal spring attached to a wall has a force constant of k = 770 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 770 N/m. A block of mass m = 1.50 kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below.

(a) The block is pulled to a position xi = 6.20 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.20 cm from equilibrium.
J

(b) Find the speed of the block as it passes through the equilibrium position.
m/s

(c) What is the speed of the block when it is at a position xi/2 = 3.10 cm?
m/s

Explanation / Answer

a) PE_max = 0.5*k*xi^2

= 0.5*770*0.062^2

= 1.48 J

b) Apply conservation of Energy

(1/2)m*v^2 = (1/2)*k*xi^2

v^2 = k*xi^2/m

v = xi*sqrt(k/m)

= 0.062*sqrt(770/1.5)

= 1.4 m/s

c) Apply conservation of energy

0.5*k*xi^2 = 0.5*k*x^2 + 0.5*m*v^2

0.5*k*xi^2 = 0.5*k*(xi/2)^2 + 0.5*m*v^2

0.5*k*xi^2 = (1/4)*0.5*k*xi^2 + 0.5*m*v^2

1.48 = 1.48/4 + 0.5*m*v^2

1.48*(1 - 1/4) = 0.5*1.5*v^2

1.11 = 0.75*v^2

==> v = sqrt(1.11/0.75)

= 1.21 m/s

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