an Atwood machine with two masses 6kg and 10kg. What is the
tension in the chord connecting the masses. Assume the pulley is
frictionless and the rope massless. Take
g=9.8m/s2
Use F = ma on each mass
If you draw it out it helps a great deal as you can fill in all the forces. Gravity acts on both and tension acts on both in the opposite direction to gravity in both cases.
The 10kg particle is going to win out so it will fall downwards (the 6kg one will move upwards)
F = ma on the 10kg particle:
Force = mass*acceleration
mg - T = ma
Gravity - Tension = the resultant force
(gravity wins out on the 10kg particle)
See if you can carry on from there. You can work out the acceleration also (although this question doesn't ask for it though but you can do it)
To find the tension in the chord connecting the masses in an Atwood machine, we can use the principle of conservation of energy.
First, let's assign a direction to each of the masses. Let's say the larger mass, 10 kg, is moving downward and the smaller mass, 6 kg, is moving upward.
The net force acting on each mass is given by the equation:
F_net = m * a
Since the pulley is frictionless and the rope is massless, the acceleration of both masses is the same and is denoted as 'a'.
Now, let's define the forces acting on each mass:
- For the 10 kg mass: The force of gravity (mg) is acting downward, and the tension in the rope is acting upward.
- For the 6 kg mass: The force of gravity (mg) is acting upward, and the tension in the rope is acting downward.
Using the second law of motion, we can write the following equations of motion:
For the 10 kg mass:
m1 * g - T = m1 * a
For the 6 kg mass:
T - m2 * g = m2 * a
Since the acceleration 'a' is the same for both masses, we can set the two equations equal to each other:
m1 * g - T = T - m2 * g
Simplifying the equation, we get:
2T = (m1 + m2) * g
Finally, we can solve for the tension in the rope:
T = ((m1 + m2) * g) / 2
Let's substitute the given values:
m1 = 6 kg
m2 = 10 kg
g = 9.8 m/s^2
T = ((6 kg + 10 kg) * 9.8 m/s^2) / 2
T = (16 kg * 9.8 m/s^2) / 2
T = 156.8 N
Therefore, the tension in the chord connecting the masses is 156.8 N.