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Teachers & SchoolsStudy Guide

1. What do we mean when we say a quantity is "conserved''?

2. What is the difference between a conservative and non-conservative force?

3. What is the difference between an elastic and an inelastic collision?

4. How do momentum and kinetic energy differ as velocity increases?

5. In an inelastic collision, when does the maximum loss of kinetic energy in the system occur?

6. Explain the work-energy theorem.

7. A 60 W incandescent light bulb draws 60 J of energy per second from your wall. Where does that energy go?

8. What is the major advantage of a hydroelectric dam over a simple waterwheel in generating electrical energy?

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9. Say you apply a force *F* to an object for a time *t* and move that object a distance *d*. How much momentum does the object have now? How much kinetic energy does it have?

10. Momentum clearly has a direction associated with it—we saw in the section on collisions that it can be positive or negative based on an object's velocity. What about energy?

1. *What do we mean when we say a quantity is "conserved''?*

Conserved quantities are those that cannot change in an isolated system, but rather must be held constant. The only way to alter the amount of a conserved quantity is by using a force that originates outside the system under consideration.

2. *What is the difference between a conservative and non-conservative force?*

Conservative forces conserve the total mechanical energy of a system. They are usually based on position, such as gravity or spring compression. Non-conservative forces, such as friction, add or remove mechanical energy from a system in the form of light, heat, sound, etc.

3. *What is the difference between an elastic and an inelastic collision?*

In an elastic collision, the kinetic energy of the objects involved is conserved; this is not true in an inelastic collision. While no real-world collision is truly elastic, many can be approximated to be, which is good enough for us (and for physicists, to be honest). In both cases, momentum is always conserved.

4. *How do momentum and kinetic energy differ as velocity increases?*

Momentum is directly proportional to an object's velocity, while kinetic energy is proportional to the square of an object's velocity. Therefore, as *v* increases, the kinetic energy of an object will increase much faster than its momentum.

5.* In an inelastic collision, when does the maximum loss of kinetic energy in the system occur?*

The maximum loss of kinetic energy occurs when two objects collide and stick together. In that case, *v*_{1,f} = *v*_{2,f}, and so the coefficient of restitution of the collision is 0.

6. *Explain the work-energy theorem.*

The work-energy theorem states that work is really just the same thing as energy; any work done on an object will change its kinetic energy by exactly the amount of energy expended doing that work. When a quarterback throws a football, the work his arm does moving the ball from behind his head to the release point is exactly equal to the kinetic energy gained by the football when it leaves his hand.

7. *A 60 W incandescent light bulb draws 60 J of energy per second from your wall. Where does that energy go?*

The energy is turned into several different forms when electricity flows through the bulb's filament: most of it is turned into light and heat, but some could also be turned into sound if the bulb is old or has a particularly noisy hum.

8. *What is the major advantage of a hydroelectric dam over a simple waterwheel in generating electrical energy?*

Dams create large lakes that are held hundreds of feet above the outlet of the river. While a waterwheel must rely purely on a river's kinetic energy to turn, a dam has stored the water up high, so that it must fall down to the turbines. This means a dam's turbines gain energy from the potential energy of millions of gallons of water held hundreds of feet in the air, not just a river's movement. ("Generating,'' by the way, is a misnomer. The law of conservation of energy means a dam—or anything else, for that matter—could never create energy, only *convert* mechanical energy into electrical energy.)

9. *Say you apply a force F to an object for a time t and move that object a distance d. How much momentum does the object have now? How much kinetic energy does it have?*

The amount of momentum gained by the object is equal to the impulse you applied to it, or *p* = *Ft*. The amount of kinetic energy gained by the object is equal to the work you did to it, or *K* = *Fd*.

10. *Momentum clearly has a direction associated with it—we saw in the section on collisions that it can be positive or negative based on an object's velocity. What about energy?*

Energy never has a direction associated with it. Potential energy is a stored quantity inherent to an object. Kinetic energy is, too, even if it's a little less obvious. Think about an object traveling to the left (negative direction) and one traveling to the right (positive direction) at exactly the same speed. When we square their velocities to find *K*, both end up with the same kinetic energy—so it would be impossible to give kinetic energy a direction. This is probably your first introduction to the idea of *scalars*, like energy, which only have a magnitude, and *vectors*, like momentum, which have both a defined magnitude and a defined direction.