A 2kg and a 4kg hang freely at opposite ends of a light inextensible string which passes over a small and light pulley fixed to a rigid support calculate the acceleration of the system
m₁a=m₁g -T
m₂a=m₂g-T
a(m₁-m₂)=g(m₁+m₂)
a =g(m₁+m₂)/(m₁-m₂)= ...
3.3
To calculate the acceleration of the system, we need to consider the forces acting on each mass.
Let's start by considering the 2 kg mass. The only force acting on it is its weight, which is given by the formula:
Weight = mass × gravity
where gravity is the acceleration due to gravity, approximately 9.8 m/s^2 on Earth.
So, the weight of the 2 kg mass is:
Weight_2kg = 2 kg × 9.8 m/s^2 = 19.6 N
Now, let's consider the 4 kg mass. Again, the only force acting on it is its weight:
Weight_4kg = 4 kg × 9.8 m/s^2 = 39.2 N
Since the masses are connected by a string passing over a pulley, they will experience the same magnitude of tension in the string.
Let's assume that the 2 kg mass moves upwards and the 4 kg mass moves downwards. In this case, the net force on the system is given by the difference between the weights:
Net Force = Weight_4kg - Weight_2kg = 39.2 N - 19.6 N = 19.6 N
Now, we can use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration:
Net Force = mass × acceleration
In this case, the net force acting on the system is the tension in the string, and the mass is the total mass of the system (2 kg + 4 kg = 6 kg).
So, we have:
Tension = Net Force = mass × acceleration
Tension = 19.6 N
mass = 6 kg
Therefore, the acceleration of the system can be calculated as:
acceleration = Tension / mass = 19.6 N / 6 kg ≈ 3.27 m/s^2
So, the acceleration of the system is approximately 3.27 m/s^2.