Work, Energy, and Power (4A) - Chem & Physics

What is the formula for mechanical work done by a constant force at angle $\theta$ to displacement?

$W = Fd\cos\theta$ . Calculates work as the component of force parallel to displacement multiplied by distance, accounting for directionality.
What is the correct expression for efficiency in terms of input and useful output energy or work?

$\eta = \frac{W_{\text{out}}}{W_{\text{in}}} = \frac{E_{\text{useful}}}{E_{\text{in}}}$ . Efficiency ratios useful output to total input, indicating the fraction of energy converted effectively without waste.
State the work–kinetic energy theorem relating net work and change in kinetic energy.

$W_{\text{net}} = \Delta K$ . Net work done on an object equals its change in kinetic energy, linking force application to motion change.
Identify the speed $v$ of an object of mass $m$ given kinetic energy $K$ in terms of $K$ and $m$ .

$v = \sqrt{\frac{2K}{m}}$ . Solving the kinetic energy formula for velocity yields this expression, relating energy directly to speed.
Identify the sign of work done by kinetic friction when an object slides a distance $d$ along the surface.

$W_f = -f_k d$ . Kinetic friction opposes motion, performing negative work by dissipating energy as heat over the distance traveled.
What is the relationship between conservative force work and potential energy change?

$W_{\text{cons}} = -\Delta U$ . Conservative forces store work as potential energy, with the negative sign indicating energy conservation in closed paths.
What is the formula for gravitational potential energy near Earth for height change $\Delta h$ ?

$\Delta U_g = mg\Delta h$ . Gravitational potential energy change arises from work against gravity, proportional to mass, gravity, and height difference.
What is the formula for average power over a time interval $\Delta t$ ?

$P_{\text{avg}} = \frac{\Delta W}{\Delta t}$ . Average power computes the mean rate of work over a finite interval.
What is the conservation of mechanical energy statement when only conservative forces do work?

$K_i + U_i = K_f + U_f$ . Mechanical energy remains constant in isolated systems with only conservative forces, as work done converts between kinetic and potential forms.
Find the gravitational potential energy increase for $m=2\ \text{kg}$ raised by $\Delta h=5\ \text{m}$ with $g=10\ \text{m}\cdot\text{s}^{-2}$ .

$\Delta U_g = 100\ \text{J}$ . Potential energy increase results from work against gravity, calculated as mass times gravitational acceleration times height change.
Find the average power if $\Delta W=600\ \text{J}$ is done in $\Delta t=3\ \text{s}$ .

$P_{\text{avg}} = 200\ \text{W}$ . Average power divides total work by time interval to determine the mean rate of energy expenditure.
Which condition makes the work done by a force exactly zero, even if $F\neq 0$ and $d\neq 0$ ?

$\theta = 90^\circ$ so $\cos\theta = 0$ . Work is zero when force is perpendicular to displacement, as no component acts along the path.
What is the formula for kinetic energy of a particle of mass $m$ moving at speed $v$ ?

$K = \frac{1}{2}mv^2$ . Kinetic energy quantifies motion, scaling with mass and the square of velocity due to work-energy principles.
What is the formula for elastic potential energy stored in an ideal spring compressed or stretched by $x$ ?

$U_s = \frac{1}{2}kx^2$ . Elastic potential energy stores deformation work in a spring, following Hooke's law with quadratic dependence on displacement.
Find the work done when $F=10\ \text{N}$ , $d=3\ \text{m}$ , and $\theta=60^\circ$ .

$W = 15\ \text{J}$ . Applies the work formula with the cosine of the angle to find the effective force component along displacement.
What is the SI unit of work, and what base units is it equivalent to?

$1\ \text{J} = 1\ \text{N}\cdot\text{m} = 1\ \text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}$ . The joule measures energy transfer, derived from force times distance, equating to base units of mass, length, and time.
What is the physical interpretation of work on a $F$ vs. $x$ graph?

Work equals the area under the $F(x)$ vs. $x$ curve. The integral of force with respect to displacement geometrically represents the net energy transfer.
What is the formula for instantaneous mechanical power delivered by a force to an object moving with velocity $\vec v$ ?

$P = \vec F\cdot\vec v$ . Instantaneous power equals the dot product of force and velocity, capturing the parallel component's contribution.
Which option gives the correct expression for work done by gravity for vertical displacement $\Delta h$ upward?

$W_g = -mg\Delta h$ . Gravity performs negative work against upward displacement, reducing potential energy gain.
What is the SI unit of power, and what is it equivalent to in base units?

$1\ \text{W} = 1\ \text{J}\cdot\text{s}^{-1} = 1\ \text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}$ . The watt quantifies power as energy per time, expressed in base units for consistency in mechanics.
What is the formula for power as the rate of doing work?

$P = \frac{dW}{dt}$ . Power measures the instantaneous rate of energy transfer through work.
What is the magnitude of static friction, and what is its maximum possible value?

$f_s\leq \mu_s N$ , with $f_{s,\max}=\mu_s N$ . Static friction adjusts to prevent motion up to a maximum determined by the coefficient and normal force.
What is the formula for work done by a variable force along a path in one dimension?

$W = \int F(x)\,dx$ . Integrates force over displacement to compute total work for non-constant forces.
What is the magnitude of kinetic friction for a block on a horizontal surface with normal force $N$ ?

$f_k = \mu_k N$ . Kinetic friction magnitude is proportional to normal force via the coefficient, assuming constant sliding motion.
What is the energy accounting equation when nonconservative work $W_{\text{nc}}$ is present?

$K_i + U_i + W_{\text{nc}} = K_f + U_f$ . Nonconservative forces introduce energy dissipation or addition, modifying the total mechanical energy balance.

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