Atwood Machine Acceleration Laboratory
Investigate Newton's Second Law of Motion using a dual-mass vertical pulley apparatus. Analyze how differential mass configurations govern system acceleration and line tension.
Pulley Mechanics Workspace View
TIME: 0.000 s
VELOCITY: 0.00 m/s
ACCELERATION: ??? m/s²
⚠️ SAFETY LIMIT: SYSTEM BLOCKED AT PULLEY HEADER
Mass Left (M1)
50 g
Consists of a 50g base hanger + added mass plates.
Mass Right (M2)
50 g
Consists of a 50g base hanger + added mass plates.
📝 Student Laboratory Instructions
1. Configure different combinations of weights on the left hanger (M1) and right hanger (M2) by clicking the mass adjuster buttons.
2. Click "Release System" to observe the acceleration under gravity (g = 9.81 m/s²). The motion will auto-brake safely when a block nears the top pulley.
3. Based on your configured mass values (M1 and M2), write down the equations of motion and solve for:
- The theoretical acceleration of the system (a) in m/s².
- The uniform tension force magnitude (T) acting within the connecting string in Newtons (N).
Calculated Acceleration (a)
0.000 m/s²
Calculated String Tension (T)
0.000 N
Mathematical Formula & Step-By-Step Derivation Matrix
1. Establish Free-Body Equations: Assuming a frictionless pulley system, let M2 > M1. Thus, M2 accelerates downwards while M1 accelerates upwards with an identical magnitude (a):
• For M1 moving upwards: T - M1g = M1a
• For M2 moving downwards: M2g - T = M2a
2. Solve for System Acceleration (a): Summing the two operational linear equations eliminates the internal line tension parameter (T):
(M2g - T) + (T - M1g) = M2a + M1a
g(M2 - M1) = a(M1 + M2)
a = g • (M2 - M1) / (M1 + M2)
3. Substitute to solve for Line Tension Force (T): Plug the isolated acceleration variable back into the M1 equation:
T = M1g + M1a = M1(g + a)
Substituting 'a' yields: T = g • (2 • M1 • M2) / (M1 + M2)
Note: Mass units must be explicitly converted from laboratory grams (g) to standard SI kilograms (kg) before calculations (1 kg = 1000 g). Earth's gravitational constant is fixed at g = 9.81 m/s².