You are working for a shipping company. Your job is to stand at the bottom of a

Question

You are working for a shipping company. Your job is to stand at the bottom of a 6.4 m -long ramp that is inclined at 40 above the horizontal. You grab packages off a conveyor belt and propel them up the ramp. The coefficient of kinetic friction between the packages and the ramp is k=0.30.

Part A

What speed do you need to give a package at the bottom of the ramp so that it has zero speed at the top of the ramp?

Part B

Your coworker is supposed to grab the packages as they arrive at the top of the ramp. But she misses one and it slides back down. What is its speed when it returns to you?

Explanation / Answer

Here ,

length of incline , L = 6.4 m

theta = 60 degree

uK = 0.30

a) let the speed at the bottom of the ramp is v

0.5 * m *v^2 = m *(g * L * sin(theta) + uK * g * L * cos(theta))

0.5 * v^2 = 9.8 * 6.4 *(sin(40) + 0.30 * cos(40))

solvng for v

v = 10.46 m/s

the speed of the package at the bottom is 10.46 m/s

b)

Now , at the bottom again

0.5 * m * (10.46^2 - vf^2) = 2 * 9.8 * 6.4 * 0.30

vf = 5.84 m/s

the speed of the package at the bottom of ramp is 5.84 m/s

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