An object of mass M = 884 g lies on a table. It is free to move along a horizontal, frictionless surface. This object is connected to a second object that hangs along the slide of the table by a massless string that runs over a pulley and connects both masses. This object has a mass of m = 890 g

Find the tension of the massless string

To find the tension in the massless string, we need to consider the forces acting on the two objects connected by the string.

1. For the object on the table (mass M):
Since the table is frictionless, the only force acting on this object is its weight (mg), pointing downward. However, since the object is not moving vertically, the vertical component of the weight is balanced by the normal force from the table.

2. For the hanging object (mass m):
The weight of this object can be broken down into two components: one along the direction of motion (m*g*sinθ) and one perpendicular to the direction of motion (m*g*cosθ). The perpendicular component does not affect the tension in the string and can be ignored.

Now, let's find the acceleration of the system:
Since the two objects are connected by a massless string and are not moving vertically, their accelerations must be the same (a). Therefore, we can equate the equations of motion for both objects:

For the object on the table:
m*a = 0 (no net force horizontally)

For the hanging object:
T - m*g*sinθ = m*a (tension minus the component of weight along the direction of motion)

We can solve these equations simultaneously to find the tension in the string (T):

From the first equation, we have:
m*a = 0
a = 0

Substituting this value of acceleration into the second equation:
T - m*g*sinθ = m*0
T - m*g*sinθ = 0
T = m*g*sinθ

Now, let's substitute the given values into the equation:
m = 890 g = 0.89 kg
g = 9.8 m/s^2 (acceleration due to gravity)
sinθ = 1 (assuming the angle θ between the string and the table is 90 degrees)

T = 0.89 kg * 9.8 m/s^2 * 1
T ≈ 8.722 N

Therefore, the tension in the massless string is approximately 8.722 N.