Forces acting on two stacked blocks

[manaXmizery]

Homework Statement

A 1.5 kg block rests on top of a 7.5 kg block which are attached using a cord to a pulley - there is no friction anywhere. What force must be applied to the bottom block so the top block accelerates to the right at 2.5 m/s^2?

Homework Equations

m1 = 1.5kg
a(to the right) = 2.5 m/s^2
m2 = 7.5kg

The Attempt at a Solution

Since we are interested in finding the horizontal force F , I neglected all the forces acting vertically on the two blocks mainly the normal Force , Fn and the weights of them . Am i right in assuming that :

1) there is no friction between the two blocks and as such , the only force acting horizontally on the top block is the tension Ft towards the right ?

2) for the bottom block , I have to assume that the force towards the left , F must be greater than the tension , Ft ?

Thanks in advance.

Regards,

Steve

 

[Orodruin]

1) Correct.

2) If F was not larger than the tension, would m2 be accelerating?

Of course, an underlying assumption that you have not mentioned is that m2 will be accelerating to the left at 2.5 m/s^2 in order for the string length to be constant.