Two masses are hung are connected by a light cord and hung from a frictionless pulley of negligible mad are shown. Mass m1=3.00kg and mass m2=2.00kg. When the two masses are released from rest, the resulting acceleration of the two masses?

mass 1 accelerates downward at a

so mass 2 accelerates up at a

tension = T

mass 1:
m g - T = m a so 3 g - T = 3 a

mass 2:
T - mg = m a so T = 2 (g+a)

substitute T in mass 1 equation
3 g - 2(g+a) = 3 a
g - 2 a = 3 a
a = g/5 = 9.81/5 = 1.962

You could also use the total mass of 5 and total force of (3-2)g

Mama

Why did the two masses go to therapy?

Because they needed to work out their acceleration issues!

To find the resulting acceleration of the two masses, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).

In this case, the force causing the acceleration is the force of gravity acting on the masses. The force of gravity can be calculated using the equation F = mg, where m represents the mass of an object and g represents the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).

Let's assign directions to the motion: Let's say m1 is moving downward and m2 is moving upward. Now, let's calculate the forces acting on each mass.

For m1:
Force of gravity acting on m1 = m1 * g = 3.00 kg * 9.8 m/s^2 = 29.4 N (downward)

For m2:
Force of gravity acting on m2 = m2 * g = 2.00 kg * 9.8 m/s^2 = 19.6 N (upward)

Now, let's find the net force on the system. Since the cord is light and frictionless, the tension in the cord is the same on both sides.

Let's assume the tension in the cord is T. For m1, the tension is acting upward, and for m2, the tension is acting downward.

Net force on the system = T - force of gravity acting on m1 + force of gravity acting on m2

Since the masses are hung from a light cord, the tension in the cord will be the same on both sides. So we can write:

Net force on the system = T - (force of gravity acting on m1) - (force of gravity acting on m2)
Net force = T - 29.4 N - 19.6 N
Net force = T - 49 N

According to Newton's second law, the net force (F) is equal to the mass (m) multiplied by the acceleration (a).

F = m1 * a (for m1)
F = m2 * a (for m2)

Since the two masses are connected by the same cord, they have the same acceleration.

Therefore, we can set the two equations equal to each other:

m1 * a = m2 * a

Canceling the acceleration on both sides of the equation, we get:

m1 = m2

Substituting the given masses into the equation:

3.00 kg = 2.00 kg

Since the equation is not valid, we can conclude that the masses do not accelerate equally. In this case, the net force is not equal to zero because the tension in the cord is greater on one side than on the other. Thus, the net force causes an acceleration in the system.

To find the resulting acceleration, we need to calculate the net force on the system divided by the total mass:

Net force = T - 49 N
Total mass (m1 + m2) = 3.00 kg + 2.00 kg = 5.00 kg

Using F = ma and rearranging the equation, we can solve for the acceleration (a):

a = (T - 49 N) / (5.00 kg)

The resulting acceleration depends on the tension in the cord (T), which we do not have information about. To determine the exact value of the acceleration, we would need the tension in the cord.

2 m/s2

1.46