ch5_adagtv

=Chapter 5 =



Section 5-1: Work
A force that causes a displacement of an object does work. **Work: ** Equal to the magnitude of the force, F, times the magnitude of the displacement. Measured in Joules (J). math \[W=F_{net}d\] math

The Joule is equal to:

math $\mathrm{N\cdot m}$ math

or:

math $\mathrm{\frac{kg\cdot m^{2}}{s^{2}}}$ math

Work is done only when components of a force are parallel to a displacement. If your force is other than horizontal, only the horizontal component of your applied force causes displacement and does work.  math \[W=F_{net}d\cos\theta\] math

<span style="color: rgb(5, 5, 5);"><span style="color: rgb(130, 251, 4);">The sign of work is important Work is positive when the component of force is in the same direction as the displacement. Work is negative when the force is in the direction opposite the displacement. If the net work is positive, the object speeds up and the net force does work //on// the object. If the net work is negative, the object slows down and work is done //by// the object on another object.

1. How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0 degrees above the horizontal? (Answer: 130 J)
 * Practice:**

<span style="font-family: Georgia,serif;">If many constant forces are acting on an object, the equation remains the same but you use the net forces and it results in the net work.

<span style="color: rgb(195, 9, 251);"><span style="font-family: Georgia,serif;">Section 5-2: Energy
math \[W_{net}=\frac{1}{2}mv^2-\frac{1}{2}mv^2\] math

<span style="font-family: Georgia,serif;"><span style="color: rgb(125, 250, 5);">Kinetic energy depends on speed and mass. <span style="color: rgb(29, 144, 252);">**Kinetic energy:** A scalar quantity that is also measured in Joules. math \[\mathit{KE}=\frac{1}{2}mv^{2}\] math

<span style="font-family: Georgia,serif;">**Kinetic energy theorem:** math \[W_{net}=\Delta \mathit{KE}\] math <span style="font-family: Georgia,serif;"><span style="color: rgb(128, 253, 33);">Potential energy is stored energy. **<span style="color: rgb(58, 148, 253);">Potential energy: ** Present in an object that has the potential to move because of its position relative to some other location. It depends not only on the properties of an object but also on the object's interaction with its environment. <span style="color: rgb(125, 251, 19);">Gravitational potential energy depends on height from a zero level. <span style="color: rgb(27, 118, 254);">**<span style="font-family: Georgia,serif;">Gravitational potential energy :** <span style="font-family: Georgia,serif;">The energy associated with an object due to the object's position relative to a gravitational source. The SI unit is the Joule. <span style="font-family: Georgia,serif;">m is the mass of the object, g is acceleration due to gravity, and h is the height of the object.

math \[PE_g=mgh\] math

<span style="font-family: Georgia,serif;"><span style="color: rgb(114, 249, 26);">Elastic potential energy depends on distance compressed or stretched. <span style="color: rgb(8, 7, 7);">The length of a spring when no external forces are acting on it is called the //relaxed length// of the spring. When the spring is compressed or stretched, elastic potential energy is stored. The amount of energy depends on the distance the spring is compressed or stretched from its relaxed length. **<span style="color: rgb(34, 137, 252);">Elastic potential energy: ** Potential energy present in a spring.

math \[\mathit{PE}_{elastic}=\frac{1}{2}kx^{2}\] math

<span style="font-family: Georgia,serif;">//k= spring constant (A flexible spring has a small spring constant, where a stiff spring has a large spring constant.)//

1. A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have? How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis ball? Answer: math \[v_{t}=1.60*10^2 \frac{m}{s}\] math This speed is much too high to be reasonable for a table-tennis ball 2. On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is .10? 3. A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight for the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling? Answer: math \[PE_{tot}=3.43*10^4 J\] math
 * Practice:**

<span style="color: rgb(203, 53, 253);"><span style="font-family: Georgia,serif;">Section 5-3: Conservation of energy
<span style="font-family: Georgia,serif;">**<span style="color: rgb(58, 118, 253);">Mechanical energy: ** The sum of kinetic energy and all forms of potential energy associated with an object or group of objects. math \[ME=KE+PE_{total}\] math

<span style="color: rgb(135, 254, 47);">Mechanical Energy is often conserved. **Conservation of mechanical energy:**

math \[ME_{i}=ME_{f}\] math

or:

math \[\frac{1}{2}mv_{i}^2+mgh_{i}=\frac{1}{2}mv_{f}^2+mgh_{f}\] math <span style="font-family: Georgia,serif;"> Energy conservation occurs when acceleration varies. On a frictionless plain, mechanical energy is conserved. <span style="font-family: Georgia,serif;"><span style="color: rgb(140, 255, 36);">Mechanical energy is not conserved in the presence of friction. 1. Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg. Answer: math \[v_{f}=7.67 \frac{m}{s} math
 * Practice:**

<span style="color: rgb(225, 52, 254);"><span style="color: rgb(225, 52, 254);">

<span style="color: rgb(225, 52, 254);"><span style="font-family: Georgia,serif;"><span style="color: rgb(225, 52, 254);">Section 5-4: Power
<span style="color: rgb(16, 15, 15);"><span style="font-family: Georgia,serif;"><span style="color: rgb(65, 127, 251);">**Power:** The rate at which work is done. Measured in watts (W). Or horsepower. <span style="color: rgb(13, 12, 12);"> <span style="font-family: Georgia,serif;"> math \[P=\frac{W}{\Delta t}=\frac{Fd}{\Delta t}=F\frac{d}{\Delta t}=Fv\] math <span style="color: rgb(5, 5, 5);"> <span style="font-family: Georgia,serif;"><span style="color: rgb(120, 253, 38);">Machines with different power ratings do the same work in different time intervals. <span style="color: rgb(5, 5, 5);"><span style="color: rgb(120, 253, 38);">