Finding acceleration of a pulley using forces?

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SUMMARY

The discussion focuses on calculating the acceleration of two blocks connected by a pulley system on a 45-degree inclined ramp. The block on the ramp has a mass of 10 kg, while the hanging block has a mass of 100 kg, and the pulley itself weighs 50 kg with a radius of 1 meter. Key equations include Torque = radius x Force x sin(theta) and Torque = Inertia of the pulley x angular acceleration, with the inertia calculated as 0.5 x Mass of the pulley x radius², resulting in 25 kg m². The user seeks assistance in determining the tensions T1 and T2 in the system to proceed with the calculations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with torque and angular acceleration concepts
  • Knowledge of inertia and its calculation for solid objects
  • Basic trigonometry, particularly sine functions
NEXT STEPS
  • Calculate the tensions T1 and T2 using the equations of motion for both blocks
  • Explore the relationship between linear acceleration and angular acceleration in pulley systems
  • Study the effects of friction on inclined planes and its impact on acceleration
  • Review examples of similar pulley problems to reinforce understanding of the concepts
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to explain pulley systems and acceleration calculations.

battosi58
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Homework Statement


alright here is the problem: a ramp that is 45 degrees angle has a block on it with mass 10 kg. then at the top of the inclined plane/ramp, there is a pulley with another block hanging down it. the mass of the hanging block is 100 kg. the mass of the pulley itself is 50kg. the radius of the pulley is 1meter. this is all i know.
i have to find the acceleration of the blocks.

Homework Equations



here are are some helpful equations: Torque=radius x Force x sin(theta)

Torque = Inertia of the pulley x angular acceleration.

inertia of the pulley = .5 x Mass of the pulley x radius^2


The Attempt at a Solution



the basic formula i am using is that R x T1 + R x T2 sin(theta) =Inertia x angular acceleration. i do not know if i am heading in the right direction.
 
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for this problem, R would be 1m, theta would be 45 degrees, inertia would be .5 x 50kg x (1m)^2= 25 kg m^2. however, i am not sure how to find T1 and T2. can anyone help me?
 

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