Two masses are held while suspended on a frictionless pulley.Their masses are 0.250 kg and 0.200 kg.

a. Compute for the acceleration of the masses once they are released?
b.Find the tension on the string

m1 accelerates upward and m2 downward

Let a be the acceleration of m1 upward and m2 downward. m2 > m1
Let T be the tension in the string connecting them. With a frictionless (and massless) pulley, the same tension force T acts upon both masses.
The equations of motion are
m2 g - T = m2 a
T - m1 g = m1 a

These two equations can be solved easily for the unknowns T and a. See what you get when you add them:
(m2 - m1) g = (m2 + m1) a
Solve that for a, and then substitute that "a" into either of the first two equations, and solve for T.

Assuming the pulleys are massless, then the force (conterclockwise positive)

Net force= m2*g -m1*g

Net force= total mass * acceleration
you know the total mass as the sum of the masses.

Tension? Consider the force pulling m1 upward:T= m1*g + m1*acceleration.

bcv

To compute the acceleration of the masses once they are released, we can use the equation:

(m2 - m1) * g = (m2 + m1) * a

Where:
m1 = mass of the first object = 0.250 kg
m2 = mass of the second object = 0.200 kg
g = acceleration due to gravity = 9.8 m/s^2

Substituting the values, we have:

(0.200 kg - 0.250 kg) * 9.8 m/s^2 = (0.200 kg + 0.250 kg) * a

(-0.050 kg) * 9.8 m/s^2 = (0.450 kg) * a

-0.49 N = 0.45 kg * a

Dividing both sides by 0.45 kg, we get:

a = -0.49 N / 0.45 kg = -1.09 m/s^2

The negative sign indicates that the acceleration is downward for the second mass.

To find the tension in the string, we can use the equation:

T = m1 * g + m1 * a

Substituting the values, we have:

T = 0.250 kg * 9.8 m/s^2 + 0.250 kg * (-1.09 m/s^2)

T = 2.45 N + (-0.2725 N)

T = 2.1775 N

Therefore, the tension in the string is 2.1775 N.

To compute the acceleration of the masses once they are released, we can use the equation m2*g - T = m2*a and T - m1*g = m1*a, where m2 is the mass of the larger mass, m1 is the mass of the smaller mass, g is the acceleration due to gravity, T is the tension in the string, and a is the acceleration.

First, we can add these two equations together to eliminate T:

(m2*g - T) + (T - m1*g) = m2*a + m1*a

Simplifying, we have:

m2*g - m1*g = (m2 + m1) * a

Next, we can solve for a:

a = (m2*g - m1*g) / (m2 + m1)

Substituting the given masses, with m1 = 0.250 kg and m2 = 0.200 kg, and the acceleration due to gravity, g = 9.8 m/s^2, we can calculate the acceleration:

a = (0.200 kg * 9.8 m/s^2 - 0.250 kg * 9.8 m/s^2) / (0.200 kg + 0.250 kg)

a = (1.96 N - 2.45 N) / 0.450 kg

a = -0.98 N / 0.450 kg

a = -2.18 m/s^2

The negative sign indicates that the acceleration is downward for the smaller mass.

To find the tension on the string, we can substitute the calculated acceleration into either of the original equations. Let's use T - m1*g = m1*a:

T - 0.250 kg * 9.8 m/s^2 = 0.250 kg * (-2.18 m/s^2)

T - 2.45 N = -0.545 N

T = -0.545 N + 2.45 N

T = 1.91 N

So, the tension in the string is 1.91 N.