You attach one end of a spring with a force constant k = 913 N/m to a wall and t

Question

You attach one end of a spring with a force constant k = 913 N/m to a wall and the other end to a mass m = 2.22 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 = 6.16 cm from equilibrium and release it.

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

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

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

Explanation / Answer

Here ,

k = 913 N/m

m = 2.22 Lg

xi = 6.16 cm

a)Potential energy stored in the spring = 0.5 * k * xi^2

Potential energy stored in the spring = 0.5 * 913 * 0.0616^2

Potential energy stored in the spring = 1.73 J

b)

let the speed of the block is v

0.5 * m * v^2 = potential energy

0.5 * 2.22 * v^2 =1.73

v = 1.25 m/s

the speed of the block is 1.25 m/s

c)

at a position x

let the velocity is v

0.5 * 2.22 * v^2 + 0.5 * 913 * x^2 = 1.73

v = sqrt((1.73 - 0.5 * 913 * x^2)* 0.9009)

the speed of the block is sqrt((1.73 - 0.5 * 913 * x^2)* 0.9009)

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