Posted by **leeece** on Sunday, October 16, 2011 at 4:58pm.

A block of mass = 0.85 kg is connected to a spring of force constant = 775N/m on a smooth, horizontal surface.

1) Plot the potential energy of the spring from = -5.00 cm to = 5.00 cm.

2) Determine the turning points of the block if its speed at x = 0 is 1.1 m/s

I am so stumped on this problem. Could someone please help?

Thank you!

- physics -
**Erica**, Monday, February 18, 2013 at 12:34am
To plot the potential energy, simply plug your givens into the equation U=(1/2)kx^2. You should get a parabola that goes to 0 in the center.

To determine the turning points of the block, use the law of conservation of energy. You know that Ui+Ki = Uf+Kf since there is no friction. At x=0, there will be no potential energy (Ui=0). A "turning point" is where the motion will stop and the block will move in the opposite direction. This means that Kf=0.

So, set Ki=Uf

(1/2)mv^2 = (1/2)kx^2

(1/2)(.9)(1.2)^2 = (1/2)(775)x^2

Solve for x=.0409 m

This will be the first turning point. The other turning point will be the opposite of this (remember the parabola) - so x=-.0409 m.

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