Atwood's Machine: Calculating Acceleration and Percent Error, Schemes and Mind Maps of Physics

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Atwood’s Machine

𝑚 1 gsinθ 𝑚 2 𝑔sinθ

θ

For mass 1

𝑥 =^ 𝑚 1 𝑔sinθ^ −^ 𝑇^ =^ 𝑚 1 𝑎 1

𝑚 1 𝑔sinθ − 𝑇 = 𝑚 1 𝑎

For mass 2

𝑥 =^ 𝑚 2 𝑔sinθ^ −^ 𝑇^ =^ 𝑚 2 𝑎 2

𝑚 2 𝑔sinθ − 𝑇 = −𝑚 2 𝑎

𝑇 − 𝑚 2 𝑔sinθ = 𝑚 2 𝑎

𝑚 1 𝑔𝑠𝑖𝑛θ − 𝑚 2 𝑔𝑠𝑖𝑛θ = 𝑚 1 𝑎 + 𝑚 2 𝑎 𝑎𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 =

𝑔𝑠𝑖𝑛θ

𝑥 1 (cm) (Position of mass 1)

(f=10Hz)

2 (𝑠 2 ) 𝑎𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 (𝑐𝑚/𝑠 2 ) 𝑎𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 (𝑐𝑚/𝑠^2 ) (By Slope) 𝑚 1 (kg) 𝑚 2 (kg) θ(°) 0 0.984 0.537 12

𝑔𝑠𝑖𝑛θ

Calculations

• 1. Find the magnitude of theoretical acceleration
• 𝑎𝑡ℎ𝑒𝑜 = 𝑚 1 −𝑚 2 𝑚 1 +𝑚 2 𝑔𝑠𝑖𝑛θ
• 2. Find the magnitude of experimental acceleration from the slope of the position vs time squared graph (𝑠𝑙𝑜𝑝𝑒 = 𝑎𝑒𝑥𝑝/ 2 )
• 3. Compare the experimental and theoretical acceleration values by calculating percent error