How Do Pulleys Affect Acceleration and Tension on an Inclined Plane?

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The discussion focuses on calculating the acceleration and tension in a system involving two 1kg masses connected by a string over a weightless pulley on a 30-degree inclined plane. The user derived the equations of motion, leading to a calculated acceleration of 2.5 m/s² and a tension of 7.5 N. There is confusion regarding an answer of 75 N provided by another source, which is suggested to be a typo. The consensus is that the user's calculations are correct, and the tension should indeed be 7.5 N. Clarification on the discrepancy in the tension value is sought, but the method used for the calculations is validated.
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Question:
A weightless pulley is attached to the top of an inclined plane which makes an angle of 30degree with the horizontal.Masses A and B,each of mass 1kg,are joined by an inextensible string passing over the pulley.Neglecting frictional forces,calculate the accleration of the masses and the tension in the string.(Shows working thanks)

My working:
let m2 be mass of b,m1 be mass of a.Assuming acceleration due to gravity to be 10m/s².
m2g - T = m2a ---(1)
T - sin30m1g = m1a ---(2)
Substituting the values from the question,i have
From (1): 10-T=a ---(3)
From (2): T-5=a ---(4)
Substitute (3) into (4):
T=7.5N
Substituting T into (3),
a=2.5m/s²

Further Details
The answers given to me was 2.5m/s² for acceleration and 75N for tension.
Is the answers correct?
If yes,any clues to get 75N?
Thanks for replying.Appreciates it.
 
Last edited:
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method looks good to me. is there a problem?
 
I would agree with mjsd, your method looks correct. I would suggest that the given answer is a typo and should read 7.5N as you have.
 

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