A block of mass 3kg which is on a smooth inclined plane making an angle of 30° to the horizontal is connected by a cord passing over a light frictionless pulley to a second block of mass 2kg hanging vertically. What is the acceleration of each block and what is the tention of thr cord?
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1.96m/s2
To find the acceleration of each block and the tension in the cord, we can analyze the forces acting on the blocks separately. Let's start with the block on the inclined plane.
Block on the Inclined Plane:
1. Resolve the gravitational force: The weight of the block acts vertically downwards. We can resolve this weight force into two components: one parallel to the inclined plane (mg * sinθ) and one perpendicular to it (mg * cosθ), where θ = 30°, and g is the acceleration due to gravity.
- Weight component perpendicular to the inclined plane: mg * cosθ = 3 kg * 9.8 m/s² * cos(30°) ≈ 25.35 N
- Weight component parallel to the inclined plane: mg * sinθ = 3 kg * 9.8 m/s² * sin(30°) ≈ 14.7 N
2. Calculate the net force parallel to the inclined plane: The net force is responsible for accelerating the block. It is equal to the weight component parallel to the inclined plane minus the frictional force.
- Frictional force: Since the inclined plane is assumed to be smooth, there is no friction acting on the block, so the frictional force is zero.
- Net force parallel to the inclined plane: 14.7 N - 0 N = 14.7 N
3. Determine the acceleration of the block: The net force parallel to the inclined plane divided by the mass of the block will give us the acceleration.
- Acceleration = Net force / Mass = 14.7 N / 3 kg ≈ 4.9 m/s²
Hanging Block:
4. Calculate the gravitational force: The hanging block experiences only the force due to gravity.
- Weight of the hanging block: mg = 2 kg * 9.8 m/s² ≈ 19.6 N
5. Determine the tension in the cord: The tension in the cord is the force that supports the hanging block. It is equal to the weight of the hanging block.
- Tension in the cord = Weight of hanging block = 19.6 N
Summary:
The acceleration of the block on the inclined plane is approximately 4.9 m/s², and the tension in the cord is 19.6 N.