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Question

The figure shows a box of mass m2 = 1.10 kg on a frictionless plane inclined at angle θ = 40°. It is connected by a cord of negligible mass to a box of mass m1 = 4.50 kg on a horizontal frictionless surface. The pulley is frictionless and massless.

(a) If the magnitude of horizontal force is 2.3 N, what is the tension in the connecting cord?
N

(b) What is the largest value the magnitude of may have without the cord becoming slack?
N

Answer 1

Where is the horizontal force? I will assume it is pushing the m1 box towards the pulley. I will also assume the 40 degrees is w/r/t horizontal and that the m2 may slide down it.
a)
A FBD of m1
2.3+T=4.5*a

and m2
1.1*9.81*sin(40)-T=1.1*a

solve for T
(2.3+T)/4.5=a

6.9363-T=1.1*(2.3+T)/4.5
(31.213-1.1*2.3)/2.1=T

T=13.659 N

b) The tension in the cord will become slack when the force is great enough to accelerate the m1 faster than m2 will slide

that a is
g*sin(40)=a
a=6.3057

plugging into m1
F=4.5*6.3057
F=28.376 N

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