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In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal
1.) the normal reaction acting between cylinder and cube is
2. acceleration of the cylinder in ground frame is?
1.) the normal reaction acting between cylinder and cube is
2. acceleration of the cylinder in ground frame is?
Most Upvoted Answer
In the adjacent figure is a cube having a smooth grove at an inclinati...
Understanding the Problem
The scenario involves a cube with a smooth groove inclined at 30 degrees, allowing a cylinder to slide without friction. The cube accelerates horizontally, and we need to determine the normal reaction force and the cylinder's acceleration in the ground frame.
1. Normal Reaction Force
- The cylinder experiences gravitational force (mg) acting vertically downward.
- The components of the gravitational force along the groove:
- Perpendicular to the groove: mg * cos(30)
- Along the groove: mg * sin(30)
- The normal reaction (N) must balance the perpendicular component of the gravitational force:
- N = mg * cos(30)
Here, m = 2 kg, g = 9.81 m/s², and cos(30) = √3/2. Thus, the normal reaction can be calculated as follows:
- N = 2 kg * 9.81 m/s² * (√3/2) ≈ 16.97 N.
2. Acceleration of the Cylinder in Ground Frame
- Since the cube accelerates horizontally with acceleration a0, the cylinder remains in equilibrium along the horizontal direction due to the absence of horizontal force acting on it.
- The cylinder will have an acceleration component down the groove due to gravity:
- a_cylinder = g * sin(30)
Given that sin(30) = 1/2, we find:
- a_cylinder = 9.81 m/s² * 1/2 = 4.905 m/s².
- This acceleration is along the incline of the groove.
Conclusion
- Normal Reaction (N) = 16.97 N.
- Acceleration of the Cylinder (in ground frame) = 4.905 m/s² down the groove.
This analysis reveals the forces at play and their effects on the cylinder within the accelerating cube.
The scenario involves a cube with a smooth groove inclined at 30 degrees, allowing a cylinder to slide without friction. The cube accelerates horizontally, and we need to determine the normal reaction force and the cylinder's acceleration in the ground frame.
1. Normal Reaction Force
- The cylinder experiences gravitational force (mg) acting vertically downward.
- The components of the gravitational force along the groove:
- Perpendicular to the groove: mg * cos(30)
- Along the groove: mg * sin(30)
- The normal reaction (N) must balance the perpendicular component of the gravitational force:
- N = mg * cos(30)
Here, m = 2 kg, g = 9.81 m/s², and cos(30) = √3/2. Thus, the normal reaction can be calculated as follows:
- N = 2 kg * 9.81 m/s² * (√3/2) ≈ 16.97 N.
2. Acceleration of the Cylinder in Ground Frame
- Since the cube accelerates horizontally with acceleration a0, the cylinder remains in equilibrium along the horizontal direction due to the absence of horizontal force acting on it.
- The cylinder will have an acceleration component down the groove due to gravity:
- a_cylinder = g * sin(30)
Given that sin(30) = 1/2, we find:
- a_cylinder = 9.81 m/s² * 1/2 = 4.905 m/s².
- This acceleration is along the incline of the groove.
Conclusion
- Normal Reaction (N) = 16.97 N.
- Acceleration of the Cylinder (in ground frame) = 4.905 m/s² down the groove.
This analysis reveals the forces at play and their effects on the cylinder within the accelerating cube.
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In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is?
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In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is?.
In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjacent figure is a cube having a smooth grove at an inclination of 30 degrees with the horizontal and its vertical face a cylinder a of mass 2 kg can slide freely inside the grove the cube is moving with constant horizontal acceleration a0 parallel to the shown face so that the cylinder does not have acceleration along horizontal1.) the normal reaction acting between cylinder and cube is2. acceleration of the cylinder in ground frame is?.
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