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.

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

Acceleration is 2.8 m/s2
T=(2m2m1/m2+m1)g
Tension is 63

Tension on string = 5 a

for 5 kg object.

9 g - Tension on string = 9 a
for 9 kg object

a is the same in both equations unless the string breaks.
Tension of spring is the same in both equations
Solve the two equations for T and a

6.3

To find the acceleration of the two objects and the tension in the string, we can consider the forces acting on each object separately and apply Newton's second law of motion.

1. Free-body diagram of the 5.00-kg object:
- There is only one force acting on the 5.00-kg object, which is the tension in the string pulling it to the right.
- Since the table is frictionless, there is no friction force.
- The weight of the object (mg) can be neglected as it cancels out when considering the tension.
- Hence, the free-body diagram of the 5.00-kg object shows a single arrow pointing to the right representing the tension in the string.

2. Free-body diagram of the 9.00-kg object:
- The only force acting on the 9.00-kg object is the weight, which acts downwards.
- There is no friction force acting horizontally as the table is frictionless.
- Hence, the free-body diagram of the 9.00-kg object shows a downward arrow representing the weight.

To find the acceleration of the two objects and the tension in the string, we can equate the net force acting on each object to its mass multiplied by its acceleration.

For the 5.00-kg object:
- The tension in the string is the net force acting on it.
- By Newton's second law, the tension is given by T = m1 * a, where m1 is the mass of the 5.00-kg object and 'a' is the acceleration.

For the 9.00-kg object:
- The weight of the object is the net force acting on it.
- By Newton's second law, the weight is given by mg = m2 * a, where m2 is the mass of the 9.00-kg object and 'a' is the acceleration.

To find the acceleration, we can set up an equation using both equations:
- T = m1 * a (equation 1)
- mg = m2 * a (equation 2)

Solve the equations by substituting the given masses:
- T = 5.00 * a
- 9.81 * 9.00 = 9.00 * a

Solving for 'a':
- 49.05 = 9a
- a ≈ 5.45 m/s²

Substitute the value of 'a' into equation 1 to find the tension (T):
- T = 5.00 * 5.45
- T ≈ 27.25 N

Therefore, the acceleration of the two objects is approximately 5.45 m/s², and the tension in the string is approximately 27.25 N.