Question

chapter 9 key equations (pages 295-296)
write the following equations according to the textbook.

write the equation for work and define all the variables.

write the equation for potential energy and define all the variables.

write the equation for kinetic energy and define all the variables.

write the equation for power and define all the variables.

Explanation:

Step1: Work Equation

The work done by a force is given by the dot product of force and displacement. For a constant force in the direction of displacement, the equation is $W = F \cdot d$, where $W$ is work, $F$ is the magnitude of the force, and $d$ is the displacement in the direction of the force.

Step2: Potential Energy (Gravitational) Equation

Gravitational potential energy is given by $PE = mgh$, where $PE$ is potential energy, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height of the object above a reference point.

Step3: Kinetic Energy Equation

Kinetic energy of an object is given by $KE = \frac{1}{2}mv^2$, where $KE$ is kinetic energy, $m$ is the mass of the object, and $v$ is the velocity of the object.

Step4: Power Equation

Power is the rate of doing work. The equation is $P = \frac{W}{t}$, where $P$ is power, $W$ is the work done, and $t$ is the time taken to do the work. It can also be written as $P = F \cdot v$ (when force and velocity are constant and in the same direction).

Answer:

• Work: $W = Fd$ ( $W$: Work, $F$: Force, $d$: Displacement in force direction )
• Potential Energy (Gravitational): $PE = mgh$ ( $PE$: Potential Energy, $m$: Mass, $g$: Acceleration due to gravity, $h$: Height )
• Kinetic Energy: $KE=\frac{1}{2}mv^{2}$ ( $KE$: Kinetic Energy, $m$: Mass, $v$: Velocity )
• Power: $P = \frac{W}{t}$ ( $P$: Power, $W$: Work, $t$: Time ) or $P = Fv$ ( $F$: Force, $v$: Velocity )