Two wooden blocks of masses 5 kg and 3 kg are connected by a massless rope. The 5 kg block is pulled by a horizontal force of 40 N.[All floors are frictionless. Ignore the vertical forces.](i) Find the acceleration of the blocks.(ii) Find the tension in the string
Question
Two wooden blocks of masses 5 kg and 3 kg are connected by a massless rope. The 5 kg block is pulled by a horizontal force of 40 N.All floors are frictionless. Ignore the vertical forces. Find the acceleration of the blocks.(ii) Find the tension in the string
Solution
(i) To find the acceleration of the blocks, we can use 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.
First, let's consider the 5 kg block. The only horizontal force acting on it is the applied force of 40 N. Therefore, the net force on the 5 kg block is 40 N.
Using Newton's second law, we can write the equation as:
Net force = mass * acceleration
40 N = 5 kg * acceleration
Simplifying the equation, we find:
acceleration = 40 N / 5 kg
acceleration = 8 m/s^2
So, the acceleration of the blocks is 8 m/s^2.
(ii) To find the tension in the string, we need to consider the forces acting on the 3 kg block. The tension in the string is the force exerted by the 5 kg block on the 3 kg block.
Since the blocks are connected by a massless rope, the tension in the string is the same for both blocks.
Using Newton's second law again, we can write the equation for the 3 kg block as:
Net force = mass * acceleration
The net force acting on the 3 kg block is the tension in the string, which is the force exerted by the 5 kg block. The mass of the 3 kg block is 3 kg.
So, we have:
Tension = 3 kg * acceleration
Tension = 3 kg * 8 m/s^2
Tension = 24 N
Therefore, the tension in the string is 24 N.
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