Me with theses 2 questions .1. describe a situation in which an object gains the same amount of gpe(gravitational potential energy) when two different paths are taken to the same point. explain (using requirements of work) why this is.2. explain what equilibrium and spring constant mean in relation to elastic potential energy. if you can with this.

1)

A inclined plane and staircase reaching the same height. Work depends on initial and final position only.

Explanation:

The amount of work done does not depend on path length. It depends on initial and final position. It is given by gravitational potential energy.

W = m g h

Where, m is the mass of the object, g is the acceleration due to gravity and h is the height.

Let the mass of the object be m. Two different paths ( one inclines plane and another staircase) are taken to same point. The object would gain same gravitational potential energy because it depends on the height through which the object is taken and not the actual path length.

W ∝ h.

2)

Spring constant can be defined as the ratio of amount of force acting spring  with the displacement caused due to the force. A deformed elastic object has elastic potential energy stored in it which is equal to the work done to deform the object. It is proportional to the spring constant and amount of stretched distance.

Equilibrium is reached when the net force acting on the spring is zero. In equilibrium state, the object has natural extension.  An object is said to possess elastic potential energy  when force is applied and object deforms relative to original equilibrium shape or length.

d is the answer i came up with

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards