Three objects are connected on the table as

Bereket

Bereket

Answered question

2022-07-21

Three objects are connected on the table as shown in Figure 5 below. The table is rough and has a coefficient of kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00 kg, as shown, and the pulleys are frictionless. Draw free-body diagrams of each of the objects. a. Determine the acceleration of each object and their directions. b. Determine the tensions in the two cords.

Answer & Explanation

Nick Camelot

Nick Camelot

Skilled2023-06-10Added 164 answers

a) To determine the acceleration of each object and their directions, we need to analyze the forces acting on each object and apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (Fnet=ma).
Let's consider each object and draw their respective free-body diagrams:
1. For the 4.00 kg object:
- The weight (due to gravity) acts downward with a magnitude of m1·g.
- The tension T1 in the cord acts to the left.
- The frictional force fk acts to the right.
Applying Newton's second law, we have:
T1fk=m1·a
2. For the 1.00 kg object:
- The weight (due to gravity) acts downward with a magnitude of m2·g.
- The tension T2 in the cord acts upward.
Applying Newton's second law, we have:
T2m2·g=m2·a
3. For the 2.00 kg object:
- The weight (due to gravity) acts downward with a magnitude of m3·g.
- The tension T1 in the cord acts to the right.
- The tension T2 in the cord acts to the left.
Applying Newton's second law, we have:
T1T2=m3·a
b) To determine the tensions in the two cords, we can use the equations obtained from applying Newton's second law to each object.
From the free-body diagram of the 4.00 kg object:
T1fk=m1·a
From the free-body diagram of the 2.00 kg object:
T1T2=m3·a
We can now solve these equations simultaneously to find the values of T1 and T2.

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