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 8.0m -long ramp that is inclined at 41? 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.

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

a)V=V0+at at the top o f the ramp

So v0=at

Since F=ma

a=Ft/m

where Ft is the total force and fd is the downward force

resulatant Vfinal=o at the top of the ramp

Ft=Fd+f

Fd=mgsin thetha

Fd=mgsin41

f=umgcos thetha

=0.30mgcos41

By first equation

Ft=mgsin41+0.30mgcos41

=mg(sin41+0.30cos41)

a=Ft/m

=mg(sin41+0.30cos41)/m

=g(sin41+0.30cos41)

=9.8(-0.15+0.30*(-0.98)

a=-4.37m/s^2

S=0.5st^2

s=8m

t=sqrt(2S/a)

=sqrt(2*8/4.37)

=1.91 sec

v0=at

=4.37*1.91

v0=8.34m/sec

b) When it slides down the force of friction f will appose the downward force Fd so we have

Ft= Fd - f then final velocity V(final) = Vf is
Vf= a t and similarly
Vf=8.34m/sec
Due to friction the initial velocity going up will be higher than final velocity coming down.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.