A 1 kg mass on a frictionless inclined plane is connected by a pulley to a hanging 5.0 kg mass,?

Question

At what angle will the system be in equilibrium? (in degrees)

1)-45
2)-30
3)30
4)45

PLEASE HELP!!

Answer 1

By drawing a sketch diagram, you can work out the system in question can be represented as a right angle triangle, with the hypotenuse equal to 1 (kg) and the opposite side = 0.5 (kg). the angle you are trying to calculate is between the hypotenuse and adjacent, and is given by the formula

sin a = opp / hyp

therefore sin a = 0.5 / 1
sin a = 0.5

a = arcsin(0.5)

a = 30 degrees.

As both weigths are acting in opposition to each other, the angle will be positive, so your answer is option 2, 30 degrees.

Hope this helps!

Answer 2

I think the data must be mixed up. Perhaps the mass on the inclined plane is 10 kg? As it is, there's no way that it could have equilibrium. Plus we would need to know how the angle is defined - is it measured from vertical or horizontal and what is the polarity convention.