2 masses m1 and m2 are connected at ends of in-extensible string that passes over pulley find acceleration and tension in pulley.
To find the acceleration and tension in the pulley, we can use Newton's second law of motion and the concept of rotational motion.
Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram of the given situation. Label the masses as m1 and m2, and denote the tension in the string as T. The string passes over the pulley.
Step 2: Write down the equations of motion
Now, let's write down the equations of motion for each mass.
For m1:
Since m1 is experiencing the force due to gravity in the downward direction and the tension T in the upward direction, we can write:
m1 * g - T = m1 * a
For m2:
Since m2 is experiencing the force due to gravity in the downward direction and the tension T in the downward direction (since the string is pulling m2 downwards), we can write:
m2 * g + T = m2 * a
Step 3: Solve the equations
Now we have two equations with two unknowns (a and T). We can solve them simultaneously to find the values.
Adding both equations, we get:
m1 * g - T + m2 * g + T = m1 * a + m2 * a
(m1 + m2) * g = (m1 + m2) * a
The masses cancel out, and we're left with:
g = a
This means that the acceleration is equal to the acceleration due to gravity g.
Using this result, we can find the tension T in the pulley. Let's substitute the value of a into either of the equations of motion. Let's use the equation for m1:
m1 * g - T = m1 * a
m1 * g - T = m1 * g
Now, isolate T:
T = m1 * g - m1 * g
T = 0
Therefore, the tension in the pulley is zero.
Step 4: Analyze the result
From our calculations, we find that the acceleration of the masses is equal to the acceleration due to gravity, and the tension in the pulley is zero. This indicates that the pulley is not rotating and the masses are not accelerating. Both masses are in equilibrium.
Note: This solution assumes an ideal situation with no friction or any other external forces acting on the system.