A mass of 9 kg while descending vertically down, drags up a mass of 6 kg by means of a string passing over a smooth pulley . find the acceleration of the system and tension in the string
summing forces about the pulley
9g-6g=15 a
solve for a
tension? 9g-6a=tension
Please don't cheat and use this website do your work and learn! - This is a troll
To find the acceleration of the system and the tension in the string, we can apply Newton's second law of motion.
First, let's define our variables:
m1 = mass of the 9 kg mass (descending)
m2 = mass of the 6 kg mass (ascending)
a = acceleration of the system
T = tension in the string
Let's start by analyzing the forces acting on each mass:
For the 9 kg mass (m1):
- Weight (mg1) = m1 * g (where g is the acceleration due to gravity)
- Tension in the string (T) acts upwards.
For the 6 kg mass (m2):
- Weight (mg2) = m2 * g
- Tension in the string (T) acts downwards.
Since the masses are connected by the same tension force, their magnitudes are equal:
T = T
Now, applying Newton's second law to each mass separately:
For m1:
m1 * a = m1 * g - T
For m2:
m2 * a = T - m2 * g
Since we want to find the acceleration of the system and the tension, we need to solve these two equations simultaneously.
First, rearrange the equations to isolate T:
T = m1 * g - m1 * a
T = m2 * g + m2 * a
Now, since the magnitudes of the two tension forces are equal (T = T), we can set the right sides of the equations equal to each other:
m1 * g - m1 * a = m2 * g + m2 * a
Next, let's rearrange the equation to isolate the acceleration (a):
m1 * g - m2 * g = m1 * a + m2 * a
g * (m1 - m2) = (m1 + m2) * a
a = g * (m1 - m2) / (m1 + m2)
This gives us the acceleration of the system.
To find the tension in the string, we can substitute the obtained acceleration value back into one of the earlier equations:
T = m1 * g - m1 * a
Substitute the known values to find the acceleration and tension.