Springs & Elastic Potential Energy Video Lessons

Example

# Problem: 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 Variablesm = 0.19 kgk = 620 N/md = 0.12 mPart (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?

###### FREE Expert Solution

Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$ Wnc 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:

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###### Problem Details

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?

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