two bodies having mass m1 of 2kg and m2 of mass 4kg are hanged with pulley. Find the acceleration and tension of the string.
To find the acceleration and tension of the string in a system where two bodies are hanging from a pulley, we can use Newton's second law and the concept of the tension force.
Let's denote the acceleration as 'a' and the tension in the string as 'T'.
1. Draw a free-body diagram for each of the masses:
- For m1 (2 kg), there are two forces acting: its weight (mg1) downwards and tension force (T) upwards.
- For m2 (4 kg), there are two forces acting: its weight (mg2) downwards and tension force (T) downwards.
2. Apply Newton's second law to each mass:
- For m1: ΣF1 = m1 * a, where ΣF1 is the net force acting on m1.
- Net force on m1 is given by: T - m1 * g = m1 * a.
- For m2: ΣF2 = m2 * a, where ΣF2 is the net force acting on m2.
- Net force on m2 is given by: m2 * g - T = m2 * a.
3. Solve the system of equations:
- T - m1 * g = m1 * a -----(1)
- m2 * g - T = m2 * a -----(2)
To find the acceleration 'a' and tension 'T', we can solve these two equations simultaneously.
4. Substitute the given values:
- m1 = 2 kg
- m2 = 4 kg
- g = acceleration due to gravity (approximately 9.8 m/s^2)
5. Solve the equations:
- Substitute m1 = 2, m2 = 4, and g = 9.8 into equations (1) and (2).
- Solve for unknowns 'a' and 'T'.
Once you solve the system of equations, you will obtain the values of acceleration 'a' and tension 'T'.