Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$ W_{nc} is the work done by non-conservative forces such as friction.

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

The potential energy of a compressed spring:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

Gravitational potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

**(a)**

Let's consider 3 potions of interest:

A student pushes a baseball of *m* = 0.19 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of *d* = 0.12 meters. The spring constant of the spring is *k* = 620 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring.**Randomized Variables**

*m* = 0.19 kg*k* = 620 N/m*d* = 0.12 m

**Part (a) ** The ball is then released. What is its speed, *v*, in meters per second, just after the ball leaves the spring?

**Part (b) ** What is the maximum height, *h*, in meters, that the ball reaches above the equilibrium point?

**Part (c) ** What is the ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Springs & Elastic Potential Energy concept. You can view video lessons to learn Springs & Elastic Potential Energy. Or if you need more Springs & Elastic Potential Energy practice, you can also practice Springs & Elastic Potential Energy practice problems.

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Based on our data, we think this problem is relevant for Professor Bompadre's class at MIZZOU.