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A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail?
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A uniform cube of side a and mass m rests on a rough horizontal table....
Introduction:
In this problem, we have a uniform cube of side length a and mass m resting on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly below the center of the face, at a height 3a/4 above the base. We need to find the minimum value of F for which the cube begins to tilt about the edge.
Analysis:
To solve this problem, we need to consider the torque acting on the cube and determine the condition for the cube to start tilting about the edge.
Torque due to the applied force:
The torque due to the applied force F can be calculated by multiplying the force F by the perpendicular distance from the point of application of force to the edge about which the cube will start tilting. In this case, the perpendicular distance is a/4, as given in the question.
Torque due to the weight of the cube:
The weight of the cube acts through its center of mass, which is located at the center of the cube. The torque due to the weight of the cube can be calculated by multiplying the weight of the cube (mg) by the perpendicular distance from the center of mass to the edge about which the cube will start tilting. In this case, the perpendicular distance is a/2, as the center of mass is at a height of a/2 above the base.
Condition for tilting:
For the cube to start tilting about the edge, the torque due to the applied force must be greater than or equal to the torque due to the weight of the cube. Mathematically, this can be expressed as:
F * (a/4) >= mg * (a/2)
Simplifying this equation, we get:
F >= 2mg
Minimum value of F:
Therefore, the minimum value of F for which the cube begins to tilt about the edge is 2mg.
Summary:
To summarize, we determined the torque due to the applied force and the torque due to the weight of the cube. By setting up the condition for tilting, we found that the minimum value of the applied force F required for the cube to start tilting about the edge is 2mg.
In this problem, we have a uniform cube of side length a and mass m resting on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly below the center of the face, at a height 3a/4 above the base. We need to find the minimum value of F for which the cube begins to tilt about the edge.
Analysis:
To solve this problem, we need to consider the torque acting on the cube and determine the condition for the cube to start tilting about the edge.
Torque due to the applied force:
The torque due to the applied force F can be calculated by multiplying the force F by the perpendicular distance from the point of application of force to the edge about which the cube will start tilting. In this case, the perpendicular distance is a/4, as given in the question.
Torque due to the weight of the cube:
The weight of the cube acts through its center of mass, which is located at the center of the cube. The torque due to the weight of the cube can be calculated by multiplying the weight of the cube (mg) by the perpendicular distance from the center of mass to the edge about which the cube will start tilting. In this case, the perpendicular distance is a/2, as the center of mass is at a height of a/2 above the base.
Condition for tilting:
For the cube to start tilting about the edge, the torque due to the applied force must be greater than or equal to the torque due to the weight of the cube. Mathematically, this can be expressed as:
F * (a/4) >= mg * (a/2)
Simplifying this equation, we get:
F >= 2mg
Minimum value of F:
Therefore, the minimum value of F for which the cube begins to tilt about the edge is 2mg.
Summary:
To summarize, we determined the torque due to the applied force and the torque due to the weight of the cube. By setting up the condition for tilting, we found that the minimum value of the applied force F required for the cube to start tilting about the edge is 2mg.
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A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail?
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A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail?.
A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force mn is applied normal to one of the faces at a point that is directly below the centre of face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is? (Assume that the cube does not slide). . Please explain in detail?.
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