1.The figure shows a box with mass m1 on a frictionless plane inclined at angle

Question

1.The figure shows a box with mass m1 on a
frictionless plane inclined at angle ?1. The box is
connected via a cord of negligible mass to another
box with mass m2 on a frictionless plane inclined at
angle ?2 (> ?1). The pulley is frictionless and has
negligible mass and assumes that the setup is on the
surface of the earth.
a) Provide free-body force diagram for both boxes.
b) What is the acceleration in terms of m1, m2, ?1 and ?2?
c) What is the tension in the cord?
d) What situation can make the acceleration to be zero and what is the tension in the
cord then?

2.A loaded penguin sled weighing 100 N rests on a plane inclined at angle 30

Explanation / Answer

1.

b) on m1 :

T - m1gsin?1 = m1a

on m2 :

m2gsin?2 - T = m2a

add both equation,

m2gsin?2 - m1gsin?1 = a(m1 + m2)

a = m2gsin?2 - m1gsin?1 / (m1 + m2)

c) T = m1gsin?1 + m1a
= m1gsin?1 + m1 (m2gsin?2 - m1gsin?1 / (m1 + m2) )

= m1^2 gsin?1 + m1m2gsin?1 + m1m2gsin?2 - m1^2 gsin?1 / (m1 +m2)

= m1m2g( sin?1 + sin?2 ) / (m1 + m2)

d) a = 0

m2gsin?2 - m1gsin?1 / (m1 + m2) = 0

m2sin?2 = m1sin?1

T = m2g ( m2sin?2 + m1sin?2) / (m1 +m2)   
= m1m2gsin?2 /(m1+ m2) or

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