
What is the significance of the negative sign in ?
Answer
417.3k+ views
Hint:Work is the measure of transfer of energy when one object is displaced from one point to another by an external force. This external force should be fully or partially directed towards the direction of displacement.
Formulae used:
where is the work done, is the force vector doing the work and is the displacement.
where is the force vector, is the mass of the body on which force is applied and is the acceleration vector.
Complete step by step answer:
Work done is the dot product of two vectors, namely Force and Displacement. Hence, work done is a scalar quantity. Therefore it is devoid of any direction.From work done equation, we have
Where is the angle between force and displacement vector.
Substituting as , we get
Acceleration here can be taken as (acceleration due to gravity) and displacement as height from the surface of the earth. Also, now becomes the angle between displacement and acceleration vector.Therefore, the equation becomes
When we consider the surface of the earth as origin and down towards the earth as positive, then any displacement from the surface of the earth to the sky will result in the angle between and to become .Now, the value of . Hence, the equation becomes
Where the negative sign denotes that work is done against gravity.
Note:This result holds true only if the body being dropped, or raised is close to the Earth’s surface. This is because as the distance from the surface of the earth increases, the magnitude of gravitational force changes. Hence the value of starts changing.
Formulae used:
where
where
Complete step by step answer:
Work done is the dot product of two vectors, namely Force and Displacement. Hence, work done is a scalar quantity. Therefore it is devoid of any direction.From work done equation, we have
Where
Substituting
Acceleration here can be taken as
When we consider the surface of the earth as origin and
Where the negative sign denotes that work is done against gravity.
Note:This result holds true only if the body being dropped, or raised is close to the Earth’s surface. This is because as the distance from the surface of the earth increases, the magnitude of gravitational force changes. Hence the value of
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