How does friction affect the acceleration of a box being pulled by a rope?

[David Donald]

Homework Statement

A box of m= 25 kg is pulled by a rope with a force of tension, F = 40 N inclined at an angle of 30o with the horizontal, there is no friction between the box and the ground.
b) Determine
the acceleration of the box.
c) Write the equation to find the acceleration
of the box in presence of a friction force of 3.0
N.
d) If a small box of 5kg with a frictional force of 2.0 N is placed against the right side of the box. Would the big box move? If so what would its acceleration be?

Please check my work and let me know if I've made any mistakes..

Homework Equations

The Attempt at a Solution

B) F = ma

(40N*Cos(30))/(25kg) = acceleration = 1.38 m/s^2

C)
∑Fx = F - Ff = ma
= (40N(cos(30) - 3N)/(25kg) = 1.26 m/s^2

d) So for this one I used the same equation I came up with in C) except mass is now 30kg because it's 25 kg box + the 5 kg box and the friction force is now 5 N

∑Fx = F - Ff = ma
= (40N(cos(30) - 5N)/(30kg) = 0.988 m/s^2

Now I don't know how to answer the word part... I would say yes it would move because their is a positive acceleration

 

[Simon Bridge]

B: did you check the vertical component ... does the box stay on the ground?
D: it seems to want you to say if the box would move without first calculating the acceleration ... i.e. compare the friction forces to the rope force.

 

[David Donald]

I'm sorry I don't quite understand how could i tell by the vertical component whether it would stay on the ground or not?

 

[Simon Bridge]

The vertical component would be how hard the rope pulls the box upwards ... is that hard enough to pull the box off the ground?