What is the relationship between work and kinetic energy for a horizontal force

Question

1. What is the relationship between work and kinetic energy for a horizontal force and displacement?
2. How might this change if the displacement is not perpendicular to the force of gravity?
3. When the ramp angle is set to any angle other than zero, how does the sign of work done by gravity compare to the work done by the applied force?
4. What is the relationship between kinetic energy and potential energy in the absence/presence of friction?

Explanation / Answer

1). for horizontal force & displacement, displacement is along the direction of applied force. so, work done by applied force = applied force*displacement work done by gravity = 0 (because displacement is perpendicular to gravity force) from work-energy theorem, work done by net forces = Change in K.E. => applied force*displacement + 0 = final K.E. - initial K.E. => Applied Force*displacement = 0.5*m*[Vf^2 - Vi^2] 2). If the displacement is not perpendicular to the force of gravity, then the gravity force will also contribute in the work calculation. applied Force*component of displacement in the direction of applied force + gravity force*component of displacement in the direction of gravity = Final K.E. - Initial K.E. => applied Force*component of displacement in the direction of applied force + gravity force*component of displacement in the direction of gravity = 0.5*m*[Vf^2 - Vi^2] 3). When the body is moving up the ramp, the work done by the gravity will be negative and the work done by applied force will be positive because the displacement of the body is in the direction of applied force & opposite to the gravity force. When the body is moving down the ramp & the applied force is along the direction of its motion, the work done by the gravity will be positive and the work done by applied force will be positive because the displacement of the body is in the direction of both applied force and the gravity force. 4). from the law of conservation of energy; Energy gained = energy lost => total change in all forms of energy = 0 In the absence of friction, change in potential energy + change in K.E. = 0 In the presence of friction, change in potential energy + change in K.E. + heat energy produced in friction = 0

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