How Do You Calculate Acceleration and Tension in a Two-Crate Pulley System?

AI Thread Summary
To calculate the acceleration of the 4.50 kg crate on the incline and the tension in the string connecting it to the 10.0 kg crate, one must analyze the forces acting on each crate. The gravitational force acting on the 4.50 kg crate can be resolved into components parallel and perpendicular to the incline, while the 10.0 kg crate experiences downward gravitational force. By applying Newton's second law, the net force on each crate can be expressed as the difference between gravitational force and tension, leading to a system of equations. Solving these equations simultaneously yields the acceleration of the 4.50 kg crate and the tension in the string. Understanding the forces involved is crucial for accurate calculations in this pulley system scenario.
SailorMoon14
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Two packing crates of masses m1 = 10.0 kg and m2 = 4.50 kg are connected by a light string that passes over a frictionless pulley as in the figure. The 4.50 kg crate lies on a smooth incline of angle 39.0°.

a) Find the acceleration of the 4.50 kg crate.

b) Find the tension in the string.

See the figure at this link: http://www.webassign.net/sf/p4_26alt.gif

I appreciate any input anyone can give me :wink:
 
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What are the forces acting on each crate?
The sum of the forces is the product mass x acceleration.
 

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