Two packing crates of masses 7.93 kg and 5.13 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 5.13 kg crate lies on a smooth incline of angle 40.0°. a) Find the acceleration of the 5.13 kg crate (b) find the tension in the string.

To find the acceleration of the 5.13 kg crate, we can use Newton's second law of motion. Let's break down the problem step by step:

Step 1: Draw a free-body diagram for each crate.
- For the 7.93 kg crate, we have the force of gravity (mg) acting downwards.
- For the 5.13 kg crate, we have the force of gravity (mg) acting downwards and a component of the force of gravity acting parallel to the incline (mg * sinθ), where θ is the angle of the incline.

Step 2: Calculate the net force on each crate.
- For the 7.93 kg crate, the net force is equal to its mass multiplied by the acceleration (F = ma).
- For the 5.13 kg crate, the net force is equal to the component of the force of gravity acting parallel to the incline (mg * sinθ) minus the tension in the string.

Step 3: Set up an equation for the system.
- Since the two crates are connected by a light string passing over a frictionless pulley, they will have the same acceleration.
- Equate the net forces on both crates and solve for the acceleration.

Step 4: Calculate the tension in the string.
- The tension in the string can be found by considering the forces acting on either side of the pulley.
- Set up an equation using the net force on each crate and solve for the tension.

Now, let's go through these steps one by one.

Step 1: Free-body diagram
- For the 7.93 kg crate, the force of gravity (mg) acts downwards.
- For the 5.13 kg crate, the force of gravity (mg) acts downwards and a component of the force of gravity acts parallel to the incline (mg * sinθ).

Step 2: Net force calculation
- For the 7.93 kg crate, the net force is equal to its mass multiplied by the acceleration (F = ma).
- For the 5.13 kg crate, the net force is equal to the component of the force of gravity acting parallel to the incline (mg * sinθ) minus the tension in the string.

Step 3: Equate the net forces
- Since the two crates are connected by a light string passing over a frictionless pulley, they will have the same acceleration.
- Equate the net forces on both crates and solve for the acceleration.

Step 4: Solve for tension
- Consider the forces acting on either side of the pulley.
- Set up an equation using the net force on each crate and solve for the tension.

Once you have the values for acceleration and tension, you can substitute them into the equations to get the final answers.

I hope this explanation helps!