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A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is:
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A particle is moving in xy plane under the action of force F such that...
Angle between Force and Linear Momentum
The angle between the force F and the linear momentum P of a particle can be determined using the dot product of the two vectors. The dot product of two vectors A and B is given by the formula A · B = |A| |B| cos θ, where θ is the angle between the two vectors.
Given Data
- Components of linear momentum: Px = 2 cos(t) and Py = 2 sin(t)
Calculating the Force Vector
Since force is the rate of change of momentum with respect to time, we can find the force vector by taking the derivative of the momentum components with respect to time:
F = dP/dt = (dPx/dt) i + (dPy/dt) j
F = (-2 sin(t)) i + (2 cos(t)) j
Calculating the Angle
To find the angle between the force and momentum vectors at any time T, we can calculate the dot product of the two vectors and divide it by the product of their magnitudes:
cos θ = (F · P) / (|F| |P|)
cos θ = [(-2 sin(t))(2 cos(t)) + (2 cos(t))(2 sin(t))] / [(√((-2 sin(t))^2 + (2 cos(t))^2)) * (√((2 cos(t))^2 + (2 sin(t))^2))]
cos θ = (-4 sin(t) cos(t) + 4 sin(t) cos(t)) / (2 * 2)
cos θ = 0
Therefore, the angle between the force and linear momentum at any time T is 0 degrees. This indicates that the force and momentum vectors are parallel to each other.
The angle between the force F and the linear momentum P of a particle can be determined using the dot product of the two vectors. The dot product of two vectors A and B is given by the formula A · B = |A| |B| cos θ, where θ is the angle between the two vectors.
Given Data
- Components of linear momentum: Px = 2 cos(t) and Py = 2 sin(t)
Calculating the Force Vector
Since force is the rate of change of momentum with respect to time, we can find the force vector by taking the derivative of the momentum components with respect to time:
F = dP/dt = (dPx/dt) i + (dPy/dt) j
F = (-2 sin(t)) i + (2 cos(t)) j
Calculating the Angle
To find the angle between the force and momentum vectors at any time T, we can calculate the dot product of the two vectors and divide it by the product of their magnitudes:
cos θ = (F · P) / (|F| |P|)
cos θ = [(-2 sin(t))(2 cos(t)) + (2 cos(t))(2 sin(t))] / [(√((-2 sin(t))^2 + (2 cos(t))^2)) * (√((2 cos(t))^2 + (2 sin(t))^2))]
cos θ = (-4 sin(t) cos(t) + 4 sin(t) cos(t)) / (2 * 2)
cos θ = 0
Therefore, the angle between the force and linear momentum at any time T is 0 degrees. This indicates that the force and momentum vectors are parallel to each other.
Community Answer
A particle is moving in xy plane under the action of force F such that...
jatin y r u acting lyk this with mukul wts wrong??
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A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is:
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A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is: for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is: covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is:.
A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is: for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is: covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in xy plane under the action of force F such that components of linear momentun P at any time T are Px=2 cos t and Py = 2 sin t. The angle between F and P at any time T is:.
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