11.50) A freight company uses a compressed spring to shoot 1.70 kg packages up a

Question

11.50) A freight company uses a compressed spring to shoot 1.70 kg packages up a 1.00-m -high frictionless ramp into a truck, as the figure(Figure 1)shows. The spring constant is 406 N/m and the spring is compressed 29.0 cm .

a) What is the speed of the package when it reaches the truck?

b) 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?

Here is a url for the figure: https://session.masteringphysics.com/problemAsset/1383422/3/11.P49.jpg

Explanation / Answer

a) Use conservation of energy:

½kx² = mgh + ½mv²

v = ( kx²/m - 2gh ) = ( (406)(0.29)² /(1.7) - 2(9.8)(1) ) = 1.37 m/s


b) No, too much energy is lost as heat caused by the friction.

½kx² = mgh + ½mv² + mgd

=1/2*406*.29^2=1.7*9.8*1+1/2*1.7*1.37^2+.300*1.7*9.8d

d=.255

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