TWO BLOCKS a AND b ARE CONNECTED BY A HEAVY ROPE OF MASS 2kg THE MASSES OF a AND b ARE 10 AND 5kg RESPECTIVELY.IF AN UPWARD FORCE OF 200N IS APPLIED TO THE TOP ROPE

A:FIND THE ACCELERATION OF THE SYSTEM
B:WHAT IS THE TENTION AT POINT P1 AND P2 ON THE HEAVY ROPE?

To solve this problem, we can apply Newton's second law of motion and consider the forces acting on the system. Let's break it down step by step:

A: FIND THE ACCELERATION OF THE SYSTEM:
1. Determine the net force acting on the system:
- The applied force acts upward on the top block, so its magnitude is 200 N.
- The weight of the blocks acts downward, so the net weight force can be calculated as:
Net weight force = (mass of block a + mass of block b) * acceleration due to gravity
= (10 kg + 5 kg) * 9.8 m/s^2
= 147 N
- The tension force in the rope also acts upward on the system.

2. Apply Newton's second law of motion:
Net force = mass * acceleration
Considering the vertical direction, the equation becomes:
200 N - 147 N = (10 kg + 5 kg) * acceleration

3. Solve for acceleration:
acceleration = (200 N - 147 N) / (10 kg + 5 kg)
= 53 N / 15 kg
= 3.53 m/s^2 (rounded to two decimal places)

Therefore, the acceleration of the system is 3.53 m/s^2.

B: WHAT IS THE TENSION AT POINT P1 AND P2 ON THE HEAVY ROPE:
To find the tension at points P1 and P2 on the heavy rope, we consider the forces acting on it.

1. Tension force at point P1:
Since block a is on top, the tension force at point P1 is equal to the applied force:
Tension at P1 = Applied force
= 200 N
Therefore, the tension at point P1 on the heavy rope is 200 N.

2. Tension force at point P2:
To find the tension at point P2, we first calculate the net force acting on block b:
Net force on block b = Applied force - Weight of block b
= 200 N - (mass of block b * acceleration due to gravity)
= 200 N - (5 kg * 9.8 m/s^2)
= 151 N

Since the heavy rope connects block a and block b, the tension force at point P2 should be equal to the net force acting on block b:
Tension at P2 = Net force on block b
= 151 N
Therefore, the tension at point P2 on the heavy rope is 151 N.