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 7.6 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?

Express your answer using two significant figures. (m/s)

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?

Express your answer using two significant figures. (m/s)

Explanation / Answer

for a mass moving up the incline plane

Fnet = m*g*sintheta + uk*m*g*costheta

from newtons law Fnet = m*a

therefore

a = g*(sintheta + uk*costheta) down the incline

a = -9.8*(sin40+0.3*cos40) = -9.23 m/s^2

if the pacakge is given a speed v up the plane, it comes to stop at the top

final speed = vf = 0

distance travelled = x = 7.6 m

from

vf^2-vi^2 = 2*a*x

0^2-v^2 = -2*9.23*7.6

v = 11.8 m/s   <<--------answer

++++++++++++++++

wen the mass slides back

Fnet = m*g*sintheta - uk*m*g*costheta

from newtons law Fnet = m*a

therefore

a = g*(sintheta - uk*costheta) down the incline

a = 9.8*(sin40-0.3*cos40) = 4.05 m/s^2

initial speed on the top = vi = 0

final speed = vf = v

distance travelled = x = 7.6 m

from

vf^2-vi^2 = 2*a*x

v^2-0^2 = 2*4.05*7.6

v = 7.85 m/s   <<--------answer

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