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 8.0-m-long ramp that is inclined at 37 degree 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 mu_k = 0.30. (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? (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

Height of ramp = 8 sin(37) = 4.8 m

friction Ff= mu)k*mg*cos(theta) = 0.3*m*g*4/5 =0.24mg

So energy conservation between two point

1/2*mv^2 = 0.24mg*8 + mg*4.8

1/2*mv^2 = 6.72 mg

v= 11.48 m/sec (ans)

b) if she misses then

mgh - mu)k*mg*cos(theta)* l = 1/2*mv^2

mg*4.8-0.24mg*8= 1/2mv^2

v= 2.4 m/sec (ans)

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