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A body undergoes a displacement of 50 m under the action of a constant force of 5 N in the same direction as that of the force. What will be the work done under the action of this force?
+ 25 J
250 J
25 J
+ 250 J
250 J
Work done is defined as the product of the magnitude of the force applied and the displacement in the direction of the force. Since the force and displacement are in the same direction, the angle between them is 0┬░, resulting in positive work.
Work done is defined as the product of the magnitude of the force applied and the displacement in the direction of the force. Since the force and displacement are in the same direction, the angle between them is 0┬░, resulting in positive work.
Pushing a trolley forward on a level floor is like this scenario; the effort you put in contributes directly to moving the object forward.
W=FтЛЕsтЛЕcos(╬╕) тАФ The general formula for work done
W=FтЛЕs тАФ Formula when force and displacement are in the same direction
According to the mechanical definition of work, W=FтЛЕsтЛЕcos(╬╕), where F is force, s is displacement, and ╬╕ is the angle between them. Given F=5┬аN, s=50┬аm, and cos(0┬░)=1, the calculation yields W=5├Ч50├Ч1=250┬аJ.
Work is a scalar quantity.
Work done is positive when force and displacement are in the same direction.
Work done is negative when force is applied opposite to displacement (e.g., friction).
The SI unit of work is Joule (J), equivalent to 1┬аNтЛЕm.
Quantifies energy transfer in mechanical systems.
Calculating the energy required to move objects.
Analyzing machine performance in mechanical engineering.
Work done is zero if force is perpendicular to displacement (e.g., 90┬░ angle).
Option A is incorrect as it results from a calculation error (50/2 or similar).
Option B and C are incorrect because they imply negative work, which would require the force to act in the opposite direction of displacement.
D is correct тАФ The work done is calculated as 5┬аN├Ч50┬аm=+250┬аJ, as force and displacement are in the same direction.
Always verify the angle between the force vector and the displacement vector; if they are parallel, use the product directly; if they are anti-parallel, the result is negative.
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