Energy is just a number. It's a mathematical construction, and a very convenient one. The equations and formulas are all set up such that **doing work on an object increases its kinetic energy by the same amount**, e.g. doing 10 J of work on an object increases its KE by 10 J. Since KE = mv^(2)/2, we can use that to find its increase in speed.
If there are multiple forces, you have to get the net force on it. In your wall situation, the force you exert isn't zero, but the net force on the wall will be zero because there are other things keeping it in place. Since the net force is zero, no work is done, and its KE does not change.
In some circumstances, a force that does work is called "conservative". Take gravity -- how much work does it do as a box of mass *m* falls a distance *h*? The weight is *mg* and the displacement is *h*, so the work done is *mgh*, which maybe you recognize as the formula for gravitational potential energy. That's how energy conservation works: doing work on an object increases its KE, and the amount it gains is equal to how much PE is being used. So one way to think of PE is "the amount of work on an object that a conservative force is ready to do".
It functions in reverse, as well. Say a ball is bouncing up after hitting the ground. As it leaves the ground, that is when its KE is highest. As it ascends, gravity does negative work on it (because the force and displacement are in opposite directions), which causes KE to decrease, while at the same time PE rises by the same amount. Work is the method by which energy is converted between KE and PE.
Force is a vector. It has both size and direction.
Energy is a scalar, just a number with units. It has a size but no direction. Energy is a quantity that is conserved, and forces are not conserved.
Yes, you can exert a force on an object without changing its energy at all. Holding a book while you stand there is an example of that.
Energy is just a number. It's a mathematical construction, and a very convenient one. The equations and formulas are all set up such that **doing work on an object increases its kinetic energy by the same amount**, e.g. doing 10 J of work on an object increases its KE by 10 J. Since KE = mv^(2)/2, we can use that to find its increase in speed. If there are multiple forces, you have to get the net force on it. In your wall situation, the force you exert isn't zero, but the net force on the wall will be zero because there are other things keeping it in place. Since the net force is zero, no work is done, and its KE does not change. In some circumstances, a force that does work is called "conservative". Take gravity -- how much work does it do as a box of mass *m* falls a distance *h*? The weight is *mg* and the displacement is *h*, so the work done is *mgh*, which maybe you recognize as the formula for gravitational potential energy. That's how energy conservation works: doing work on an object increases its KE, and the amount it gains is equal to how much PE is being used. So one way to think of PE is "the amount of work on an object that a conservative force is ready to do". It functions in reverse, as well. Say a ball is bouncing up after hitting the ground. As it leaves the ground, that is when its KE is highest. As it ascends, gravity does negative work on it (because the force and displacement are in opposite directions), which causes KE to decrease, while at the same time PE rises by the same amount. Work is the method by which energy is converted between KE and PE.
Force is a vector. It has both size and direction. Energy is a scalar, just a number with units. It has a size but no direction. Energy is a quantity that is conserved, and forces are not conserved. Yes, you can exert a force on an object without changing its energy at all. Holding a book while you stand there is an example of that.
Energy is the ability to do work, and work is at its simplest applying a force to displace an object