Two masses M1 = 6.10 kg and M2 = 3.90 kg are on a frictionless surface, attached by a thin string. A force of 47.7 N pulls on M2 at an angle of 29.5° from the horizontal as shown in the figure. Calculate the tension T in the string.

To calculate the tension T in the string, we can apply Newton's second law of motion.

Step 1: Resolve the force F into its horizontal and vertical components.
- The horizontal component of the force F is F_h = F * cos(angle).
- The vertical component of the force F is F_v = F * sin(angle).
- Given F = 47.7 N and angle = 29.5°, we can calculate F_h and F_v.

F_h = 47.7 N * cos(29.5°)
F_v = 47.7 N * sin(29.5°)

Step 2: Determine the net force acting on each mass.
- For mass M1, the only force acting on it is the tension T in the string.
- For mass M2, the net force is the combination of the horizontal component of force F and the tension T. Since the surface is frictionless, there is no friction.

Net force on M1 (F_net1) = T
Net force on M2 (F_net2) = F_h + T

Step 3: Apply Newton's second law of motion to each mass.
- Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
- The acceleration of each mass is the same since they are connected by a string and move together.

F_net1 = M1 * a
F_net2 = M2 * a

Step 4: Equate the expressions for the net forces and solve for T.
- Since M1 and M2 have the same acceleration a, we can set the expressions for F_net1 and F_net2 equal and solve for T.

T = F_h + T - M1 * a

Step 5: Substitute the known values and solve for T.
- Substitute the values from step 1 and M1 = 6.10 kg, M2 = 3.90 kg into the equation from step 4. Then solve for T.

T = F_h + T - M1 * a
T - T = F_h - M1 * a
0 = F_h - M1 * a
T = F_h / (1 + M1 / M2)

- Substituting the values, we get:

T = (47.7 N * cos(29.5°)) / (1 + 6.10 kg / 3.90 kg)

Now, plug these values into a calculator to find the tension T in the string.