A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging 9.00-kg object. Draw free-body diagrams of both objects. Find the acceleration of the two objects and the tension in the string.

Ignore the pulley's moment of inertia (since they don't tell you its radius and mass). Let T be the unknown tension on both sides.

With two equations, the variable T can be eliminated to solve for the acceleration, which is the same for both masses.

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draw a free body diagram for each object hen use newtons 2nd law then let the t variable be the unknown and add the 2 equations after finding the acceleration you are then capable of solving the equation

To find the acceleration of the two objects and the tension in the string, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration.

First, let's draw the free-body diagram for the 5.00-kg object on the table:
1. Draw a dot to represent the object.
2. Draw an arrow pointing upward to represent the force of gravity acting on the object. Label it as 'mg', where 'm' is the mass of the object (5.00 kg) and 'g' is the acceleration due to gravity (9.8 m/s^2).
3. Draw an arrow pointing to the right to represent the tension in the string. Label it as 'T'.

Next, let's draw the free-body diagram for the 9.00-kg hanging object:
1. Draw a dot to represent the object.
2. Draw an arrow pointing downward to represent the force of gravity acting on the object. Label it as 'mg', where 'm' is the mass of the object (9.00 kg) and 'g' is the acceleration due to gravity (9.8 m/s^2).
3. Draw an arrow pointing to the left to represent the tension in the string. Label it as 'T'.

Now, let's apply Newton's second law of motion to the two objects:
For the 5.00-kg object on the table:
The net force acting on this object is equal to its mass times its acceleration. Therefore, we have:
T - mg = ma, where 'm' is the mass of the object (5.00 kg), 'g' is the acceleration due to gravity (9.8 m/s^2), 'T' is the tension in the string, and 'a' is the acceleration of the system.

For the 9.00-kg hanging object:
The net force acting on this object is equal to its mass times its acceleration. Therefore, we have:
mg - T = ma, where 'm' is the mass of the object (9.00 kg), 'g' is the acceleration due to gravity (9.8 m/s^2), 'T' is the tension in the string, and 'a' is the acceleration of the system.

Solving these two equations simultaneously will allow us to find the acceleration of the system and the tension in the string.