1. B. the ability to do work

In fact, energy is exactly defined as the ability to do work: for example, if the gravitational potential energy of an object is 100 J, it means that it can converts this energy into work done.

2. The form of energy changes, but the total energy remains the same

The law of conservation of energy states that the energy cannot be created nor destroyed, but only transformed into different forms: in this case, the electrical energy due to the current inside the circuit is converted into radiant energy, due to the light emitted by the lamp, but the total energy remains the same.

3. 30,000 J

The work done when the force of F=300 N pushes the box for a distance of d=100 m is given by the product between the two:

W=Fd=(300 N)(100 m)=30,000 J

4. leaning against a brick wall on the side of a building

This is not an example of work, because work is defined as the product between the force F and the displacement d:

W=Fd

however, in this case no displacement occurs, so d=0 and W=0.

5. They change the strength or direction of a force.

In fact, simple machines (like pulleys or levers) generally work by multiplying the input force, so that it is able to move/lift a much larger force.

6. Less force is applied over a longer distance.

By using levers, the force is applied over a longer distance. This means that a less force can be used: in fact, the momentum applied is given by

M=Fd

where F is the force applied and d is the distance of the force from the fulcrum: by increasing d, the distance, a less force F can be applied, keeping the same value of momentum M.

7. Heat is the flow of thermal energy from one object to another.

In fact, heat is related to how much thermal energy flows between two objects. Thermal energy, instead, refers to the amount of energy due to the random motion of the molecules inside an object, and it is proportional to the temperature of the object.