When you do to lift an object and then release it, the energy converts back to as the object falls. This process appears similar to the storage and release of elastic that we learned about in the previous chapter and suggests that we define a (). It’s not obvious where gravitational potential energy is stored, but for our purposes can treat it as being stored within the system comprised of the Earth and the objects we are moving around. The , and are forms of . Forces and corresponding that convert energy between forms of mechanical energy within a system are known as and . We introduce these new terms because there are many cases when only conservative forces are acting and so energy just transfers between the forms of within the system. For such cases, any increase in potential energy is offset by a decease in kinetic energy and vice versa, so we know . do that converts between , , or (we will learn more about chemical potential energy soon). , , , forces caused by muscular contractions, and forces resulting in permanent deformation are examples of non-conservative forces.
Calculate the you must do to raise 10 kg metal ball by a height of 10 m.
Work is a transfer of energy, in this case in your body was transferred to what type of energy?
Was this a ?
If you then dropped the ball, what would the object have just as it reached the ground (ignoring any work done by so that only acts on the ball)? [Hint: Are there any non-conservative forces acting during the fall?]
What would be the of the ball immediately before impact with the ground?
Check out this simulation, which shows how energy is transferred among different types.
Conservation of Energy
Considering the we expect that any change to the total energy of a system must correspond to energy being transferred to the system from outside the system by an external net work on the system. Our observations have confirmed this expectation and are summarized by the :
Gravitational Potential Energy
According to the , if we do to lift an object farther from the Earth without increasing its or we must have increased the gravitational potential energy by the same amount as the work. The we need to apply is the object’s , or () and the distance we over which we apply the force is the change in height . Therefore the we did was: and this must be the same the amount that we have changed the gravitational potential energy.
Note that the previous equation automatically gives a decrease in gravitational potential energy when an object gets lower because the change in height will be negative. The work done to lift an object is an example of , or work done on the outside environment.
Calculate the change in when you climb 10 m high set of stairs.
How much did you do while climbing the stairs?
Your body is not 100% efficient, so you actually did a bunch of additional work that didn’t increase your , but increased instead. We will learn more about your body’s in the next unit.
Everyday Example: Rock Climbing Fall
A rock climber is 3.5 m above their last anchor point and fall. They will fall back 3.5 m back to the anchor point and then another 3.5 m below it before the rope comes tight for a total fall distance of 7.0 m (there was 3.5 m of rope out when they fell, so they will have to end up hanging by 3.5 m of rope). Neglecting , how fast will they be moving when the rope begins to come tight?
We will apply the during the fall.
Neglecting there are no forces other than on the person during the fall, so only are acting and is conserved:
Next we write out the changes in each type of energy:
We recognize the initial was zero at the start of the fall and that we can divide every term in our equation by mass to cancel it out:
Then we isolate the speed:
Finally we take the square root:
The climber fell 7.0 m, so the change in height was actually -7.0 m. We are ready to calculate the final speed:
The climber in the example problem above will be caught by the rope. Do you think the rope should be designed to stretch so the catch occurs over a long distance or a short one? Explain.
What is the of the climber just as the rope begins to come tight?
How much work must be done by the rope in order to bring the climber to a stop?
If the rope stretches by 0.50 m while catching the climber, what is the average force applied to the climber? This type of stretchy dynamic rope is used in rock climbing. The rope only slightly elastic, (the climber doesn’t bounce back up to nearly their original height). The rope is designed so that system has a small and most of the energy in the fall is transferred into thermal energy during the process of stretching the rope.
If a static rope was used, so the stretch was only 0.05 m while catching the climber, what is the average force applied to the climber? This type of non-stretchy static rope should not be used for rock climbing.
- OpenStax, College Physics. OpenStax CNX. May 13, 2019 http://firstname.lastname@example.org ↵
A quantity representing the effect of applying a force to an object or system while it moves some distance.
energy which a body possesses by virtue of being in motion, energy stored by an object in motion
the energy stored within an object, due to the object's position, arrangement or state. Examples are gravitational potential energy due to the relative position of masses and elastic potential energy caused by being under stress
potential energy stored in objects based on their relative position within a gravitational field
energy stored in the deformation of a material
the sum of potential and kinetic energy
forces that do work which converts energy between forms of mechanical energy (potential energy and kinetic energy)
work that converts energy between mechanical forms of energy (potential energy and kinetic energy)
forces that do non-conservative work, which is work that does not transfer energy only among kinetic and potential forms (mechanical energy)
energy stored in the microscopic motion of atoms and molecules (microscopic kinetic energy)
energy stored in the chemical bonds of a substance
a force that acts on surfaces in opposition to sliding motion between the surfaces
a force applied by a fluid to any object moving with respect to the fluid, which acts opposite to the relative motion of the object relative to the fluid
a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid
distance traveled per unit time
Energy cannot be created or destroyed, only transferred from one type to another and/or from one object to another
the net work on a system must be equal to the sum of the changes in kinetic, potential, and thermal energies
any interaction that causes objects with mass to change speed and/or direction of motion, except when balanced by other forces. We experience forces as pushes and pulls.
the force of gravity on on object, typically in reference to the force of gravity caused by Earth or another celestial body
work done on the external environment, such as moving objects, as apposed to work done internally, such as pumping blood
ratio of useful work performed to total energy expended
a measurement of the amount of matter in an object made by determining its resistance to changes in motion (inertial mass) or the force of gravity applied to it by another known mass from a known distance (gravitational mass). The gravitational mass and an inertial mass appear equal.
the fraction of relative velocity remaining after a collision, for collision with a stationary object equal to the ratio of final speed to initial speed