- Part A A freight company uses a compressed spring to shoot 1.90 kg packages up

Question

- Part A 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 384 N / In and the spring is compressed 32.0 cm. What is the speed of the package when it reaches the truck? Express your answer with the appropriate units. HA 6 + 0 2 ? Value Units Submit Request Answer Part 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? Figure 50-cm-long sticky spot

Explanation / Answer

Spring potential energy is converted Kinetic energy + potential energy of the package. So, 1/2*384*0.32^2= 1/2*1.9*v^2+ 1.9*9.8*1

So, v^2= 19.66-18.62 / 0.95

So, speed of the package when it reaches the truck is v= 0.24m/s

Now, a part of the initial Spring potential energy of 1/2*384*0.32^2 = 19.66J is converted to heat in the friction , which is given by friction coefficient * normal reaction * distance covered = 0.3*1.9*9.8*0.5 = 2.8J

So, at the start of the frictionless ramp, the Kinetic energy of the package is now 19.66-2.8= 16.86J

and change in potential energy required for the package to reach the truck is 1.9*9.8*1= 18.62J

So, energy required is 18.62J but energy available is 16.86J. So, the next package will not make it to the truck.

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