a frictionless mass1(1kg) is accelerated by mass two(1kg). The two masses are conceted by inextensible,flexible string. calculate the acceleration of the system of the two masses.
Perhaps mass 2 is hanging from a pulley on earth and mass one is sliding on a frictionless horizontal table?
If so
force = m2 g
mass accelerated = (m1+m2)
F = m a
m2 g = (m1+m2) a
To calculate the acceleration of the system consisting of two masses connected by an inextensible, flexible string, we can consider the forces acting on each mass.
Let's assume mass 1 (m₁) experiences an acceleration (a) in the positive direction, and mass 2 (m₂) is being pulled by that same string. Since the string is inextensible and flexible, the magnitude of the acceleration experienced by both masses will be the same.
Now, let's consider the forces acting on mass 1 (m₁). The only force acting on it is the tension (T) in the string pulling it towards the positive direction.
Using Newton's second law (F = m * a), we can write:
T - m₁ * g = m₁ * a₁
Where T is the tension in the string and g is the acceleration due to gravity. Since the system is frictionless, there is no frictional force acting on either mass.
Now, let's consider the forces acting on mass 2 (m₂). The only force acting on it is the tension (T) in the string pulling it towards the negative direction.
Using Newton's second law again, we have:
m₂ * g - T = m₂ * a₂
Since the tension in the string is the same for both masses, T = m * a, where m = m₁ = m₂ (mass of both masses).
Combining both equations, we have:
T - m * g = m * a
m * g - T = m * a
Adding the two equations together, the tension cancels out:
m * g - m * g + T - T = m * a + m * a
0 = 2m * a
2m * a = 0
Therefore, the acceleration of the system is 0 m/s².
In this case, the net force acting on the system is zero, resulting in zero acceleration. The tension in the string simply balances out the force due to gravity for each mass, causing them to remain stationary or move together without any acceleration.