Physics Flashcards: Analyze Energy Using Conservation Laws

What this deck covers

This deck focuses on Analyze Energy Using Conservation Laws, giving you a quick way to review the definitions, rules, and examples that matter most for Physics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify the correct energy equation for a pendulum bob between two heights when air resistance is negligible.

Answer: $mgh_i+\frac{1}{2}mv_i^2=mgh_f+\frac{1}{2}mv_f^2$. Conservation of mechanical energy for pendulum motion.

Flashcard 2: Find the speed $v$ of a mass $m$ after descending height $h$ with kinetic friction doing work $-f_k d$.

Answer: $v=\sqrt{2gh-\frac{2f_k d}{m}}$. Apply energy conservation with friction work included.

Flashcard 3: What is the gravitational potential energy formula near Earth for mass $m$ at height $h$?

Answer: $U_g=mgh$. Weight ($mg$) times height gives gravitational potential energy.

Flashcard 4: State the conservation of mechanical energy equation when only conservative forces act.

Answer: $K_i+U_i=K_f+U_f$. Total mechanical energy remains constant with only conservative forces.

Flashcard 5: Find the speed $v$ after dropping from rest through height $h$ with no losses.

Answer: $v=\sqrt{2gh}$. From $mgh = \frac{1}{2}mv^2$ with energy conservation.

Flashcard 6: Identify the correct energy equation for a block starting from rest: slide down height $h$ with friction work $W_f$.

Answer: $mgh+W_f=\frac{1}{2}mv^2$. Initial PE plus friction work equals final KE.

Flashcard 7: What is the general energy accounting equation including nonconservative work?

Answer: $K_i+U_i+W_{nc}=K_f+U_f$. Includes nonconservative work in energy conservation.

Flashcard 8: What is the general energy accounting equation including nonconservative work $W_{\text{nc}}$?

Answer: $K_i+U_i+W_{\text{nc}}=K_f+U_f$. Nonconservative work accounts for energy not conserved.

Flashcard 9: What is the relationship between nonconservative work and mechanical energy change?

Answer: $W_{nc}=\Delta E_{mech}$. Nonconservative work equals the change in total mechanical energy.

Flashcard 10: Find the speed at the bottom after dropping from rest through height $h$, ignoring air resistance.

Answer: $v=\sqrt{2gh}$. From $mgh=\frac{1}{2}mv^2$, solving for $v$ gives $\sqrt{2gh}$.

Flashcard 11: Find the speed $v$ at height $h$ for an object launched upward with speed $v_0$ (no air drag).

Answer: $v=\sqrt{v_0^2-2gh}$. Energy conservation: $\frac{1}{2}mv_0^2=\frac{1}{2}mv^2+mgh$.

Flashcard 12: Find the spring compression $x$ needed to stop a mass $m$ moving at speed $v$ on a frictionless surface.

Answer: $x=v\sqrt{\frac{m}{k}}$. All kinetic energy converts to spring PE: $\frac{1}{2}mv^2=\frac{1}{2}kx^2$.

Flashcard 13: What is the work–energy theorem relating net work and kinetic energy change?

Answer: $W_{net}=\Delta K$. Net work equals the change in kinetic energy.

Flashcard 14: State the work–energy theorem relating net work and kinetic energy change.

Answer: $W_{\text{net}}=\Delta K$. Net work equals the change in kinetic energy.

Flashcard 15: What is the kinetic friction magnitude formula using coefficient $\mu_k$ and normal force $N$?

Answer: $f_k=\mu_k N$. Kinetic friction equals coefficient times normal force.

Flashcard 16: Find the minimum initial speed $v_0$ needed to reach height $h$ if nonconservative work is $W_{nc}<0$.

Answer: $v_0=\sqrt{2gh-\frac{2W_{nc}}{m}}$. Rearrange energy equation with negative nonconservative work.

Flashcard 17: Find the final speed $v_f$ if net work on a mass $m$ is $W_{net}$ and initial speed is $v_i$.

Answer: $v_f=\sqrt{v_i^2+\frac{2W_{net}}{m}}$. From work-energy theorem: $W_{net} = \frac{1}{2}m(v_f^2 - v_i^2)$.

Flashcard 18: Find the work done by friction $W_f$ if mechanical energy decreases from $E_i$ to $E_f$.

Answer: $W_f=E_f-E_i$. Friction work equals the mechanical energy loss.

Flashcard 19: Find the maximum height $h$ reached by an object launched upward with initial speed $v_0$ (no air drag).

Answer: $h=\frac{v_0^2}{2g}$. From $\frac{1}{2}mv_0^2=mgh$, solving for $h$ gives $\frac{v_0^2}{2g}$.

Flashcard 20: What conservation equation applies when only conservative forces do work on a system?

Answer: $K_i+U_i=K_f+U_f$. Mechanical energy is conserved when only conservative forces act.

Flashcard 21: Identify the correct expression for mechanical energy lost to friction over distance $d$ on level ground.

Answer: $\Delta E_{mech}=-\mu_k N d$. Friction force times distance gives energy lost.

Flashcard 22: What is the elastic potential energy formula for a spring with constant $k$ stretched by $x$?

Answer: $U_s=\frac{1}{2}kx^2$. Spring energy equals half the spring constant times displacement squared.

Flashcard 23: What is the definition of total mechanical energy $E_{mech}$ in a system?

Answer: $E_{mech}=K+U$. Total mechanical energy is the sum of kinetic and potential energies.

Flashcard 24: Identify the sign of $\Delta U_g$ when an object moves downward by $\Delta h<0$.

Answer: $\Delta U_g<0$. Moving down means $\Delta h<0$, so $mg\Delta h<0$.

Flashcard 25: Find the height $h$ reached if an object launched upward with speed $v_0$ stops at the top (no losses).

Answer: $h=\frac{v_0^2}{2g}$. From $\frac{1}{2}mv_0^2 = mgh$ at maximum height.

Flashcard 26: What is the work done by a constant force $F$ over displacement $d$ at angle $\theta$?

Answer: $W=Fd\cos\theta$. Work equals force times displacement times cosine of angle between them.

Flashcard 27: Find the speed $v$ of mass $m$ after sliding down height $h$ with kinetic friction $\mu_k$ over distance $d$.

Answer: $v=\sqrt{2g(h-\mu_k d)}$. Initial PE minus friction work equals final KE.

Flashcard 28: Choose the correct statement: with only conservative forces, mechanical energy is (constant) or (decreases).

Answer: Mechanical energy is constant. Conservative forces don't dissipate energy.

Flashcard 29: What is the kinetic energy formula for a mass $m$ moving at speed $v$?

Answer: $K=\frac{1}{2}mv^2$. Energy of motion equals half the mass times velocity squared.

Flashcard 30: What is the gravitational potential energy change when an object drops by height $h$?

Answer: $\Delta U_g=-mgh$. Negative because potential energy decreases when falling.

Flashcard 31: Identify the correct condition for using $mgh$ for gravitational potential energy.

Answer: Near Earth with approximately constant $g$. $mgh$ assumes constant gravitational field strength.

Flashcard 32: Find the minimum initial speed $v_0$ to reach height $h$ if a constant friction force $f_k$ acts over distance $d$.

Answer: $v_0=\sqrt{2gh+\frac{2f_k d}{m}}$. Initial KE must overcome both PE gain and friction work.

Flashcard 33: What is the gravitational potential energy change near Earth for height change $\Delta h$?

Answer: $\Delta U_g=mg\Delta h$. Weight $mg$ times height change gives gravitational PE change.

Flashcard 34: Find the final speed $v$ if net work done on mass $m$ is $W_{\text{net}}$ and initial speed is $v_i$.

Answer: $v=\sqrt{v_i^2+\frac{2W_{\text{net}}}{m}}$. From work-energy theorem: $W_{\text{net}}=\frac{1}{2}m(v^2-v_i^2)$.

Flashcard 35: Find the compression $x$ of a spring that stops a mass $m$ moving at speed $v$ on a frictionless surface.

Answer: $x=v\sqrt{\frac{m}{k}}$. From $\frac{1}{2}mv^2 = \frac{1}{2}kx^2$ by energy conservation.

Flashcard 36: Which option is correct for a conservative force: $W_c=-\Delta U$ or $W_c=+\Delta U$?

Answer: $W_c=-\Delta U$. Conservative force work equals negative of potential energy change.

Flashcard 37: What is the sign of work done by kinetic friction on a moving object over distance $d$?

Answer: $W_f=-f_k d$. Friction opposes motion, so work is negative.

Flashcard 38: What is the elastic potential energy stored in a spring with constant $k$ stretched by $x$?

Answer: $U_s=\frac{1}{2}kx^2$. Spring PE equals half the spring constant times displacement squared.

Flashcard 39: What is the work done by kinetic friction with coefficient $\mu_k$ over distance $d$ on level ground?

Answer: $W_f=-\mu_kmgd$. Friction opposes motion, so work is negative.