# Problem: 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?

###### FREE Expert Solution

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:

U0 + KE0 + Wnc= Uf + KEf + wf

Wnc 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/s2

f = μkmg

###### Problem Details

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?