I have this very confusing two part question that i am having trouble understanding.

For the first question i first created a free body diagram to show the forces acting on both the boxes.

However i am unsure of what to do after this since i don't understand how to use newtons second law to find acceleration for this acceleration.

From what i think i understand you need to sum all of newtons forces on the first box and get t on one side of the equation then plug in t for the equation for the sum of the forces on the second box and then get a (acceleration) by itself. but i am not sure how to do this.

the second part (b) is also confusing since i don't understand the first part of this question.

below is the questions a and b.

two blocks are connected by a string that passes over a friction less pulley. mass m1 sits on a plane inclined to and angle of 30 degrees above the horizontal and mass m2 hangs freely over the edge of the inclined plane.

a)assuming the plane is frictionless determine the acceleration of the system in terms of the masses and the angle of the plane

b) if m=m2=10kg determine the coefficient of friction necessary to keep the masses stationary.

To solve this problem, we will break it down into two parts: handling the forces acting on the system and applying Newton's second law. Let's start with part (a).

a) To determine the acceleration of the system, we need to consider the forces acting on each block individually. Here's what you can do step by step:

1. Draw a free body diagram for both blocks. This will help us visualize the forces acting on each block. For m1, we have two forces: the weight force (mg) acting vertically downwards, and the normal force (N) perpendicular to the incline. For m2, we only have the weight force (mg) acting downwards.

2. Resolve the weight force into components along the incline and perpendicular to it. Since the angle of the incline is given as 30 degrees, the weight force component along the incline for m1 is mg * sin(30°), and the weight force component perpendicular to the incline is mg * cos(30°).

3. Apply Newton's second law to each block. For m1, the net force along the incline is given by m1 * g * sin(30°) - T = m1 * a, where T is the tension in the string and a is the acceleration of the system. For m2, the net force acting downwards is T - m2 * g = m2 * a (since m2 hangs freely).

4. Solve the two equations simultaneously. We have two unknowns (T and a), but we can eliminate T by equating its value in both equations. Solving the system of equations will allow us to find the acceleration (a) in terms of the masses (m1, m2) and the angle of the plane.

b) Now, let's move on to part (b) where we need to determine the coefficient of friction necessary to keep the masses stationary. In this case, the acceleration is zero since the masses are stationary. We need to find the maximum friction force (F) and the normal force (N) acting on m1.

1. Draw a free body diagram for m1. The weight force (mg) acts downwards, and the normal force (N) and friction force (F) act perpendicular and parallel to the incline, respectively.

2. Resolve the weight force into components along the incline and perpendicular to it, similar to step 2 in part (a).

3. Apply Newton's second law perpendicular to the incline. Since the block is stationary, the sum of the vertical forces is zero. So, N - mg * cos(30°) = 0. This equation allows us to find the normal force (N).

4. Apply Newton's second law parallel to the incline. Since the block is stationary, the sum of the horizontal forces is also zero. So, F - mg * sin(30°) = 0. This equation allows us to find the maximum friction force (F).

5. Finally, use the equation for static friction, which is given by F = μs * N, where μs is the coefficient of static friction. We can substitute the values of F and N found in steps 3 and 4, and solve for μs.

I hope this explanation helps you in understanding the steps to solve this problem. If you have any further questions, please feel free to ask!