A 15kg ball hangs by a string from the roof of a 20kg box. The box is attached b

Question

A 15kg ball hangs by a string from the roof of a 20kg box. The box is attached by a rope to a 10kg rock over a very light frictionless pulley. There is no appreciable friction between the box and the table it rests on.

What is the tension in the rope? (Newtons)

What angle does the string make with the vertical?

What is the tension in the string? (Newtons)

If you could vary the weight of the rock what is the maximum angle the string could make with the vertical?

Please show all work necessary to complete the problem. Thanks in advance!

Explanation / Answer

let the acceleration be a then

a=10g/(10+20+15)=2.18m/s^2

10g-T=10a

T=76.3N

using non inertial reference for string and applyin pseudo force= 15a

for equilibrium

T1sin=15a

T1cos=15g

dividing both and solving we get

=12.53 degrees

T1=150.73N

max angle will be when rock weight =

in that case a will be equal to g and

tan=1

=45degrees

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