You attach one end of a spring with a force constant k = 833 N/m to a wall and t

Question

You attach one end of a spring with a force constant

k = 833 N/m

to a wall and the other end to a mass

m = 1.42 kg

and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position

xi = 6.76 cm

from equilibrium and release it.

(a) Determine the potential energy stored in the spring before the block is released.
J

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

(c) Determine the speed of the block when it is at a position

xi/4. m/s

Explanation / Answer

part a )

U = kx^2/2

x =xi = 6.76 cm = 6.76 x 10^-2 m

U = 1.9 J

part b )

using energy conservation

total energy = KE + PE

kA^2/2 = mv^2/2 + kx^2/2

A = 6.76 cm

at x = 0 total potential energy convert into kinetic energy

1.9 = mv^2/2

v = 1.64 m/s

part c )

x = xi/4 = 6.76/4 = 1.69 cm

1.9 = mv^2/2 + 1/2 * 833 * (1.69 x 10^-2)^2

v = 1.58 m/s

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