Energy lost by the friction created is:
W = - μkmgd = - (0.300)(1.90)(9.81)(50.0 × 10-2) = - 2.8 J
The final kinetic and potential energy is:
Ef = KE + PE = (1/2)mv2 + mgh
W = ΔEmech
Therefore, W = (1/2)mv2 + mgh - Ep.s
(1/2)mv2 = W - mgh + Ep.s
v2 = sqrt[2(W - mgh + Ep.s)/m]
A freight company uses a compressed spring to shoot 1.90-kg packages up a 1.00-m-high frictionless ramp into a truck, as the figure (Figure 1) shows. The spring constant is 378 N/m and the spring is compressed 33.0 cm.
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 package make it into the truck? ( Yes or No?)
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