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The work done by the force is defined to be
- a)the product of force and the magnitude of the displacement
- b)the negative product of component of the force in the direction of the displacement and the magnitude of this displacement
- c)the product of component of the force in the direction perpendicular to displacement and the magnitude of the displacement
- d)the product of component of the force in the direction of the displacement and the magnitude of the displacement
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The work done by the force is defined to bea)the product of force and ...
Explanation:Work done is given by
W = (Fcosθ)d
here Fcosθ is the component of applied force in direction of displacement and d is magnitude of displacement.
Most Upvoted Answer
The work done by the force is defined to bea)the product of force and ...
According to these options correct answer is ( D) because option-a is not clear explanation about diffination of work . option-b is not available for all condition and option-c is wrong .
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The work done by the force is defined to bea)the product of force and ...
The Work Done by a Force
The work done by a force is a fundamental concept in physics that describes the transfer of energy from one object to another. It is defined as the product of the component of the force in the direction of the displacement and the magnitude of the displacement.
Explanation:
To understand why the correct answer is option 'D', let's break down the components of the force and displacement.
Force:
A force is a push or pull that can cause an object to accelerate or change its state of motion. Forces can be applied in different directions and at various angles relative to a reference point. In this context, we consider the force applied in the same direction as the displacement.
Displacement:
Displacement refers to the change in position of an object. It is a vector quantity that includes both magnitude and direction. In this case, we consider the displacement in the same direction as the force.
Work Done:
Work done by a force is a measure of the energy transferred to an object as a result of the force acting on it. Mathematically, it is calculated as the dot product of the force and displacement vectors.
Dot Product:
The dot product of two vectors is a scalar quantity calculated by multiplying the magnitudes of the vectors and the cosine of the angle between them. For the work done calculation, we consider the angle between the force vector and the displacement vector to be zero degrees, indicating that they are in the same direction.
Calculation:
Using the dot product formula, the work done (W) can be expressed as:
W = F · d · cosθ
where F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors (which is zero degrees in this case).
When the angle is zero degrees, the cosine of 0° is 1. Therefore, the equation simplifies to:
W = F · d
This equation confirms that the work done by a force is equal to the product of the component of the force in the direction of the displacement and the magnitude of the displacement, as stated in option 'D'.
Therefore, the correct answer is option 'D'.
The work done by a force is a fundamental concept in physics that describes the transfer of energy from one object to another. It is defined as the product of the component of the force in the direction of the displacement and the magnitude of the displacement.
Explanation:
To understand why the correct answer is option 'D', let's break down the components of the force and displacement.
Force:
A force is a push or pull that can cause an object to accelerate or change its state of motion. Forces can be applied in different directions and at various angles relative to a reference point. In this context, we consider the force applied in the same direction as the displacement.
Displacement:
Displacement refers to the change in position of an object. It is a vector quantity that includes both magnitude and direction. In this case, we consider the displacement in the same direction as the force.
Work Done:
Work done by a force is a measure of the energy transferred to an object as a result of the force acting on it. Mathematically, it is calculated as the dot product of the force and displacement vectors.
Dot Product:
The dot product of two vectors is a scalar quantity calculated by multiplying the magnitudes of the vectors and the cosine of the angle between them. For the work done calculation, we consider the angle between the force vector and the displacement vector to be zero degrees, indicating that they are in the same direction.
Calculation:
Using the dot product formula, the work done (W) can be expressed as:
W = F · d · cosθ
where F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors (which is zero degrees in this case).
When the angle is zero degrees, the cosine of 0° is 1. Therefore, the equation simplifies to:
W = F · d
This equation confirms that the work done by a force is equal to the product of the component of the force in the direction of the displacement and the magnitude of the displacement, as stated in option 'D'.
Therefore, the correct answer is option 'D'.
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The work done by the force is defined to bea)the product of force and the magnitude of the displacementb)the negative product of component of the force in the direction of the displacement and the magnitude of this displacementc)the product of component of the force in the direction perpendicular to displacement and the magnitude of the displacementd)the product of component of the force in the direction of the displacement and the magnitude of the displacementCorrect answer is option 'D'. Can you explain this answer?
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