Show that change in kinetic energy due to friction is given by ∆K = − f k d where k f is friction acting on an object and d is the length of the path followed by an object

Question

nick1337 · Accepted Answer

To show that the change in kinetic energy due to friction is given by ∆K = -fkd, we can use the work-energy theorem and the definition of work done by friction.The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by friction on the object is equal to the change in its kinetic energy.The work done by friction can be calculated using the formula:Wfriction=fkdcos(θ),where fk is the magnitude of the frictional force, d is the length of the path followed by the object, and θ is the angle between the direction of the frictional force and the displacement of the object.In this case, the object is moving in the direction of the frictional force, so the angle θ between the force and the displacement is 0 degrees. Therefore, cos(θ)=1.Substituting this into the equation for work done by friction, we have:Wfriction=fkdSince the work done by friction is equal to the change in kinetic energy, we can write:Wfriction=ΔKTherefore, we have:ΔK=fkdBut the work done by friction is opposite in direction to the motion of the object, so it is negative. Therefore, we can write:ΔK=−fkdHence, we have shown that the change in kinetic energy due to friction is given by ΔK=−fkd.

Show that change in kinetic energy due to

Answered question

Answer & Explanation

New Questions in Advanced Physics