Concept #1: Conservation of Total Energy

Concept #2: Conservation of Mechanical Energy

Example #1: Conservation of Energys

Concept #3: The Conservation of Energy Equation

Example #2: Using the Energy Equation

Concept #4: Using the Energy Equation

Example #3: Using the Energy Equation

The potential energy between two identical atoms has the form U(x) = A / x 10 − B / x5 where x is the separation distance between the atoms and A and B are constants with appropriate units. The two atoms, initially very far apart, are released from rest. What is the maximum kinetic energy that each of the two atoms can have?
1. Kmax = (A2 / 2B)
2. Kmax = (B2 / 4A)
3. Kmax = (A2 / 8B)
4. Kmax = (A / 4)
5. Kmax = (B2 / 2A)
6. Kmax = 0
7. Kmax = (B / 8)
8. Kmax = (B2 / 8A)
9. Kmax = (A2 / 4B)
10. Kmax = (B)

Is it possible for a system to have negative potential energy?
A. Yes, as long as the total energy is positive.
B. Yes, since the choice of the zero of potential energy is arbitrary.
C. No, because this would have no physical meaning.
D. Yes, as long as the kinetic energy is positive.
E. No, because the kinetic energy of a system must equal its potential energy.

When an object moves from A to point B, gravity does positive work on the object. When the object from point A to point B, its gravitational potential energy
A) stays the same
B) increases
C) decreases

A 150 g object starts on the ground, is moved 1.2 m in the +x direction over a frictionless surface, is then moved upwards 50 cm, then moved in a straight line back to its starting position. How much work does gravity do during this motion?

Swimmers at water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide I compare with v 2, the speed of a swimmer reaching the end of slide 2?
A) v1 > v2
B) v1 < v2
C) v1 = v2
D) The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses.
E) No simple relationship exists between v1 and v2.

You and your friend, who weighs the same as you, want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top.
A) It is impossible to tell, since the times you both took are unknown.
B) It is impossible to tell, since the distances you both traveled are unknown.
C) You friend's gravitational potential energy is greater than yours, because he got to the top faster.
D) Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance getting to the top.
E) Both of you have the same amount of gravitational potential energy at the top.

Object A is stationary while objects B and C are in motion. Forces from object A do
16 J
of work on object B and -5 J
of work on object C. Forces from the environment do 4 J
of work on object B and 8 J
of work on object C. Objects B and C do not interact.What is tot if objects A, B, and C are defined as separate systems?What is tot if one system is defined to include objects A, B, and C and their interactions?What is int if objects A, B, and C are defined as separate systems?What is int if one system is defined to include objects A, B, and C and their interactions?

is the energy bar chart for a firefighter sliding down a fire pole from the second floor to the ground. Let the system consist of the firefighter, the pole, and the earth.
Suppose
E1 = 14.What is the bar height of Wext?What is the bar height of pandoc:
Error at "source" (line 1, column 17):
unexpected "{"
expecting letter or new-line
K_{
m f hspace{1 pt}}?What is the bar height of UGf?

A 72.0-kg swimmer jumps into the old swimming hole from a diving board 3.25 m above the water.Use energy conservation to find his speed just as he hits the water if he just holds his nose and drops in.Use energy conservation to find his speed just as he hits the water if he bravely jumps straight up (but just beyond the board!) at 2.50 m/s.Use energy conservation to find his speed just as he hits the water if he manages to jump downward at 2.50 m/s.

A man with mass exttip{m}{m} sits on a platform suspended from a movable pulley, as shown in the figure , and raises himself at constant speed by a rope passing over a fixed pulley. The platform and the pulleys have negligible mass. Assume that there are no friction losses.Find the force he must exert.Find the increase in the energy of the system when he raises himself a distance exttip{x}{x}. (Answer by calculating the increase in potential energy.)Find the increase in the energy of the system when he raises himself exttip{x}{x}. (Answer by computing the product of the force on the rope and the length of the rope passing through his hands.)

The lowest point in Death Valley is 85 m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 m above sea level.What is the change in potential energy of an energetic 72 kg hiker who makes it from the floor of Death Valley to the top of Mt. Whitney?

What is the kinetic energy of a 1700 kg car traveling at a speed of 30 m/s ( 65)?From what height would the car have to be dropped to have this same amount of kinetic energy just before impact?Does your answer to part B depend on the car’s mass?

With what minimum speed must you toss a 160 g ball straight up to just touch the
13-m-high roof of the gymnasium if you release the ball 1.4 m above the ground? Solve this problem using energy.With what speed does the ball hit the ground?

A 1500 kg car traveling at 16 m/s suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll.You may want to review (Pages 234 - 238).For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car rolling down a hill.What will be the car’s speed as it coasts into the gas station on the other side of the valley?

Jane, looking for Tarzan, is running at top speed (4.8 m/s ) and grabs a vine hanging vertically from a tall tree in the jungle.How high can she swing upward?Does the length of the vine affect your answer?

The maximum height a typical human can jump from a crouched start is about 60.0 cm .By how much does the gravitational potential energy increase for a 71.0 kg person in such a jump?Where does this energy come from?

An astronaut on earth can throw a ball straight up to a height of 16 m .How high can he throw the ball on Mars?

A 12 kg mass is moving down a frictionless incline under the influence of gravity. If the incline has a height of 1 m, and an incline angle of 35°, how much work is done by gravity as the mass slides down the surface? What is the kinetic energy of the mass at the bottom of the incline?

At time t i, the kinetic energy of a particle is 30.0 J and the potential energy of the system to which it belongs is 10.0 J. At some later time tf, the kinetic energy of the particle is 18.0 J.(a) If only conservative forces act on the particle, what are the potential energy and the total energy of the system at time tf?(b) If the potential energy of the system at time tf is 5.00 J, are any nonconservative forces acting on the particle?(c) Explain your answer to part (b).

A 6.0 kg monkey swings from one branch to another 1.5 m higher. What is the change in gravitational potential energy?

A system loses 660 J of potential energy. In the process, it does 660 J of work on the environment and the thermal energy increases by 160 J. Find the change in kinetic energy K.

(a) How much work is done by the environment in the process shown in the figure?(b) Is energy transferred from the environment to the system or from the system to the environment?

Consider the process shown in the figure below. Suppose E1 = 3 J. What is the final kinetic energy of the system for the process shown in the figure?

In one day, a 85 kg mountain climber ascends from the 1520 m level on a vertical cliff to the top at 2420 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1310 m.(a) What is her change in gravitational potential energy on the first day?(b) What is her change in gravitational potential energy on the second day?

A ball of mass m falls from a height h to the floor.(a) Write the appropriate version of Equation 8.2 for the system of the ball and the Earth and use it to calculate the speed of the ball just before it strikes the Earth.(b) Write the appropriate version of Equation 8.2 for the system of the ball and use it to calculate the speed of the ball just before it strikes the Earth.

A 0.20-kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone–Earth system (a) before the stone is released and (b) when it reaches the bottom of the well? (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?