The cart experiences a frictional force which is directly proportional to its weight. This means that there must be a force applied on the car to balance the forces on the car to produce a net force of 0.
This is in accordance to Newton's first law which states that an object at rest will remain at rest and an object in motion will remain in motion unless an external force acts on it. The force must be a resultant force.
Therefore, the force needed increases with the total weight of the cart as well as with the added mass in a linear manner.
The answer is A) 1000 J
According to the law of conservation of energy, the total energy before an action is always equal to the total energy after the action.
So that is, the total energy is 8000J found as potential energy, 7000J has transformed into kinetic energy, then the thermal energy should be the remaining 1000J.
Hope this helps.