Question

Derive the formula for work done by a constant force.

Answer 1

work done=component of force in the directiom of displacement × magnitude of displacement.

W=F cos theta ×s

W=Fs cos theta

W=F(vector).S(vector)

Answer 2

Answer:

Work done by a constant force (W) = F × D.

Explanation:

"Work done by a constant force is defined as the product of the displacement of an object with constant force applied on it, that is parallel to the direction of displacement.

• Work is calculated in Joules.
• Joule is also called a Newton-meter (N.m), this is equivalent to kg.m²/s².
• If an object is displaced by a force in its direction, then the done is called positive work.
• Example: When a ball fall towards the ground where the displacement of the ball is the same as the direction of the gravitational force.
• When a force acts on any object and if there is displacement, then it means that work has been done over the object.
• Physically, when work is done on the object is the change in the kinetic energy, it is the energy that an object experiences.
• Derivation: A block placed on a frictionless horizontal floor acted by a constant force F due to which there is movement in the block. This block moves through a distance d in a straight line in the direction of the force.  
• The work done by force F is equal to the change in kinetic energy.

• W = (1/2)mv² - (1/2) mu² = 1/2m(v²-u²)
• Applying v²-u² = 2as
• W = (1/2)m(2as)
• W = mas
• According to Newton's second law: F = ma
• Thus W = Fs. (s=d=displacement)
• The effective component of force along with the direction of displacement Fcosθ, which is responsible for the displacement of the object in the direction given.
• Then work done (W) by the force (F) in displacing the body through displacement (d)

• W = (Fcos θ)d

W = Work done on the object.

F = Magnitude of the force that is applied.

d = Magnitude of the displacement in the direction of the force.

θ = is the angle between force and displacement

SI unit of work is Joule (J).

Hence, The formula for work done is W = (Fcos θ)d.