Spring potential energy:

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

Kinetic Energy:

$\overline{)\begin{array}{rcl}\mathbf{K}\mathbf{.}\mathbf{E}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}{\mathbf{mv}}^{\mathbf{2}}\end{array}}$

Gravitational potential energy:

$\overline{)\begin{array}{rcl}{\mathbf{U}}& {\mathbf{=}}& \mathbf{m}\mathbf{g}\mathbf{h}\end{array}}$

Conservation of energy:

**U _{0} + KE_{0} + W_{nc}= U_{f} + KE_{f}**

W_{nc} is the work done by non conservative forces.

- d = 50.0 cm(1m/100cm) = 0.5m
- μ = 0.300
- m = 1.70 kg
- h = 1.0 m
- k = 341N/m
- x = 33.0 cm(1m/100cm) = 0.33m
- g = 9.8 m/s
^{2}

f = μ_{k}mg

A freight company uses a compressed spring to shoot 1.70 kg packages up a 1.00 m-high frictionless ramp into a truck. The spring constant is 341 N/m and the spring is compressed 33.0cm.

A careless worker spills his soda on the ramp. This creates a 50.0 cm-long sticky spot with a coefficient of kinetic friction 0.300. Will the next package make it into the truck?

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.