Question

Two blocks of masses m1=3kg and m2=5kg connected by a rope of negligible mass and slide on a frictionless surface. A force of 10 N acts on m2 at a 20 degree angle to the horizontal. Find a) the acceleration of m1 as well as it's orientation b) the tension in the rope.

The diagram is similar to that in this linked image: http://gauss.vaniercollege.qc.ca/pwiki/images/a/aa/N_APP_EX_4.png

Answer 1

a)

$m_2a=Fcos20\degree-T$

$m_1a=T-m_1gsin37\degree$

$a(m_1+m_2)=Fcos20\degree-m_1gsin37\degree$

$a=\frac{Fcos30\degree-m_1gsin37\degree}{m_1+m_2}=\frac{10cos20\degree-3\cdot9.8sin37\degree}{3+5}=-1.04$ m/s²

direction is to right side

b)

$T=Fcos20\degree-m_2a=10cos20\degree+5\cdot1.04=14.6$ N