Respuesta :
Let's address each part of the question:
(i) The energy of the object A at point Y can be determined using the work-energy principle. The work done by the opposing force is equal to the change in kinetic energy of the object.
Given:
Initial kinetic energy (K.E) at X = 800 N
Opposing force (F) = 100 N
Distance XY = 2 m
Work done by the opposing force (W) = force × distance = 100 N × 2 m = 200 J
Change in kinetic energy = Work done by the opposing force
K.E at Y - K.E at X = -200 J (negative because the force opposes the motion)
K.E at Y = K.E at X - 200 J = 800 J - 200 J = 600 J
Therefore, the energy of the object A at point Y is 600 J.
(ii) To find the further distance where the object A comes to rest, we can use the work-energy principle again. At rest, the kinetic energy of the object is zero.
Let the distance from Y to the point where the object comes to rest be d meters.
The work done by the opposing force from Y to the point where the object comes to rest is equal to the change in kinetic energy:
Work done = force × distance = 100 N × d
Since the object comes to rest, the change in kinetic energy is equal to the negative of the final kinetic energy at Y:
Change in kinetic energy = -600 J
Therefore, we have:
100 N × d = -600 J
Solving for d:
d = -600 J / 100 N = -6 m
Since distance cannot be negative, the object comes to rest 6 meters further from point Y.
(iii) Yes, the work done by the opposing force is negative. This is because the force opposes the direction of motion of the object. According to the work-energy principle, when a force opposes the direction of motion, the work done by that force is negative. In this case, the force acts in the opposite direction of the displacement of the object (from X to Y), resulting in negative.
Summary:
Energy at Y: -200 J
Distance to rest: 2 meters
Work done by opposing force: Negative due to opposite direction of motion.
