an object on an inclined ramp of mass 1.39kg. The angle of the inclined surface is 29deg with the horizontal. The object on the ramp is connected to a second object of mass 2.17kg on a horizontal surface below an overhang that is formed by the inclined surface. Further, an external force of magnitude 9.00N is exerted on the object on the ramp. We observe both objects to accelerate. Assuming that the surfaces and the pulley are frictionless, and the connecting string and the pulley are massless, what is the tension in the string connecting the two objects?

m1•a=F-T-m1•g•sinα

m2•a=T
(m1+m2)a= F-T-m1•g•sinα+T
a=(F-m1•g•sinα)/(m1+m2).
T=m2•a=m2• (F-m1•g•sinα)/(m1+m2)=...

To find the tension in the string connecting the two objects, we can start by analyzing the forces acting on each object individually and then use Newton's second law to relate the tensions.

1. Object on the ramp:
The only force acting on the object on the ramp is the external force of magnitude 9.00N, which is exerted parallel to the ramp. This force causes the object to accelerate down the incline.

The force of gravity acting on the object can be resolved into two components: one parallel to the ramp (mg*sin(θ)) and one perpendicular to the ramp (mg*cos(θ)), where m is the mass of the object and θ is the angle of the inclined surface.

2. Object on the horizontal surface:
The force of gravity acting on the object is mg, which acts vertically downwards. Since the surface is frictionless, there is no horizontal force acting on this object.

Now, let's apply Newton's second law to both objects separately:

1. Object on the ramp:
The equation of motion in the direction parallel to the ramp is:
9.00N - mg*sin(θ) = (m1)*a1, where a1 is the acceleration of the object on the ramp.

2. Object on the horizontal surface:
The equation of motion in the vertical direction is:
mg - T = (m2)*a2, where a2 is the acceleration of the object on the horizontal surface.

Since the string connecting both objects is massless, the tension in the string is the same for both objects, so we can simply denote it as T.

Now, we can relate the accelerations of the two objects using the fact that they are connected by the string passing over the pulley:

a2 = -a1, where the negative sign indicates that the objects have opposite directions of acceleration.

Now, we can substitute this relation into the equation of motion for the object on the horizontal surface and solve for T:

mg - T = (m2)*(-a1)
T = mg + (m2)*a1

Substituting the value of a1 from the equation of motion for the object on the ramp, we get:

T = mg + (m2)*(9.00N - mg*sin(θ))/(m1)

Finally, plugging in the given values:
m1 = 1.39kg
m2 = 2.17kg
θ = 29 degrees

We can calculate the tension in the string using these values.