A freight company uses a compressed spring to shoot 1.60 kg packages up a 1.00-m

Question

A freight company uses a compressed spring to shoot 1.60 kg packages up a 1.00-m -high frictionless ramp into a truck, as the figure(Figure 1) shows. The spring constant is 357 N/m and the spring is compressed 30.0 cm. What is the speed of the package when it reaches the truck? Express your answer with the appropriate units. 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?

Explanation / Answer

part A)

speed of the package is v

spring constant , k = 357 N/m

mass , m = 1.6 Kg

compression , x = 30 cm

x = 0.30 m

let the speed at the top is v m/s

Using work eenergy theorum

0.5 * m * v^2 = 0.5 * k * x^2 - m * g * h

0.5 * 1.6 * v^2 = 0.5 * 357 * 0.30^2 - 1.60 * 9.8 * 1

v = 0.69 m/s

the speed of the package at the top is 0.69 m/s

part B)

For the distance , d = 50 cm = 0.50 m

coefficient of friction , u = 0.30

Using work energy theorum

0.5 * m * v^2 = 0.5 * k * x^2 - m * g * h - u * mg * d

0.5 * 1.6 * v^2 = 0.5 * 357 * 0.30^2 - 1.60 * 9.8 * 1 - 0.30 * 1.6 * 9.8*0.50

solving for v

v = -1.568 i

as the velocity is imaginary ,

NO , the block will not reach the top of the ramp

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