A horizontal spring attached to a wall has a force constant of k = 900 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 900 N/m. A block of mass m = 1.10 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 = 5.20 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 5.20 cm from equilibrium.

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

-i1 ponts SerCP11 13.PU21. Ny Noles Ask Your T A horizontal sprinq attached to wall hes force constart of K = you Nfrn. A block of mass m = 1.10 kg attached tu te spring dnd rests on d frictionless, horizontal surface as in the ficure below x-0-x2 x-x (a) The block is pulled to positionXi-5.20 cm from aquíbrium and rclaassd. Fnd the potential energy stored in thc spring who thc block is 5.20 cm from aquiloriun. d Find the potential cnergy Find the speed of the block as it passes through the equiiun positin. What is the speed of the block when it is at a poition x2 2.00 cm Need Help? L NOTE

Explanation / Answer

This is an energy balance problem since there is no friction.

Change in energy of the system = 0
Change in energy of the system = 1/2*k*(xf^2 - xi^2) + 1/2*m*(vf^2 - vi^2)

a) When the spring is stretch/compressed by 5cm all the energy is stored as potential in the spring.
Total energy = 1/2*k*x^2 = 1/2* 900 N/m * (.052 cm) ^2 = 1.216 J

b) When it passes through the equilibrium point, all the spring energy is transferred into kinetic energy and the velocity is max

1.216J = 1/2 * m * v^2
v = sqrt(2* 1.216 J / m ) = 1.55 m/s

c) At xi/2 = 2.60 cm you have part of the energy still in spring potential and part in kinetic energy
Remember, the change in energy = 0 = 1/2*k*(xf^2 - xi^2) + 1/2*m*(vf^2 - vi^2)

1/2*k*(xi^2 - xf^2) = 1/2 * m * (vf^2 - vi^2)

vi = 0 m/s

1/2*900 N/m * ( (.052 m)^2 - (.026 m)^2 ) = 1/2* 1.10 kg *vf^2

vf = sqrt(900 N / m / 1.10 kg * (.00270 m^2 - .000676 m^2) ) = 1.48 m/s

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