Model Energy Transfer Computationally - Physics
Card 1 of 30
Find average power for $\Delta E=600,\text{J}$ transferred in $\Delta t=3,\text{s}$.
Find average power for $\Delta E=600,\text{J}$ transferred in $\Delta t=3,\text{s}$.
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$200,\text{W}$. $P = \frac{600}{3} = 200,\text{W}$
$200,\text{W}$. $P = \frac{600}{3} = 200,\text{W}$
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Find $K$ for $m=2,\text{kg}$ and $v=3,\text{m/s}$ using $K=\frac{1}{2}mv^2$.
Find $K$ for $m=2,\text{kg}$ and $v=3,\text{m/s}$ using $K=\frac{1}{2}mv^2$.
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$9,\text{J}$. $K = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9,\text{J}$
$9,\text{J}$. $K = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9,\text{J}$
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What is the gravitational potential energy function for two masses separated by distance $r$?
What is the gravitational potential energy function for two masses separated by distance $r$?
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$U=-\frac{Gm_1m_2}{r}$. Negative sign indicates attractive force lowers PE as $r$ decreases.
$U=-\frac{Gm_1m_2}{r}$. Negative sign indicates attractive force lowers PE as $r$ decreases.
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Identify the computational update rule for speed from kinetic energy $K$ and mass $m$.
Identify the computational update rule for speed from kinetic energy $K$ and mass $m$.
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$v=\sqrt{\frac{2K}{m}}$. Rearranged kinetic energy formula to solve for speed.
$v=\sqrt{\frac{2K}{m}}$. Rearranged kinetic energy formula to solve for speed.
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What is the thermal energy change formula for heating with no phase change?
What is the thermal energy change formula for heating with no phase change?
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$Q=mc\Delta T$. Heat transfer depends on mass, specific heat, and temperature change.
$Q=mc\Delta T$. Heat transfer depends on mass, specific heat, and temperature change.
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Find $\Delta U_g$ for $m=4,\text{kg}$, $\Delta h=2,\text{m}$, $g=10,\text{m/s}^2$.
Find $\Delta U_g$ for $m=4,\text{kg}$, $\Delta h=2,\text{m}$, $g=10,\text{m/s}^2$.
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$80,\text{J}$. $\Delta U_g = (4)(10)(2) = 80,\text{J}$
$80,\text{J}$. $\Delta U_g = (4)(10)(2) = 80,\text{J}$
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Find spring energy $U_s$ for $k=200,\text{N/m}$ and $x=0.10,\text{m}$.
Find spring energy $U_s$ for $k=200,\text{N/m}$ and $x=0.10,\text{m}$.
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$1,\text{J}$. $U_s = \frac{1}{2}(200)(0.1)^2 = \frac{1}{2}(200)(0.01) = 1,\text{J}$
$1,\text{J}$. $U_s = \frac{1}{2}(200)(0.1)^2 = \frac{1}{2}(200)(0.01) = 1,\text{J}$
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Find work $W$ for $F=10,\text{N}$, $d=5,\text{m}$, and $\theta=60^\circ$.
Find work $W$ for $F=10,\text{N}$, $d=5,\text{m}$, and $\theta=60^\circ$.
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$25,\text{J}$. $W = (10)(5)\cos(60°) = 50(0.5) = 25,\text{J}$
$25,\text{J}$. $W = (10)(5)\cos(60°) = 50(0.5) = 25,\text{J}$
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What equation relates energy transferred by heating to mass, specific heat, and temperature change?
What equation relates energy transferred by heating to mass, specific heat, and temperature change?
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$Q=mc\Delta T$. Heat capacity relates thermal energy to temperature change.
$Q=mc\Delta T$. Heat capacity relates thermal energy to temperature change.
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What is the net work–kinetic energy relation used to compute speed changes?
What is the net work–kinetic energy relation used to compute speed changes?
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$W_{\text{net}}=\Delta K$. Work-energy theorem: net work changes kinetic energy.
$W_{\text{net}}=\Delta K$. Work-energy theorem: net work changes kinetic energy.
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What is the kinetic energy formula used in energy-transfer calculations?
What is the kinetic energy formula used in energy-transfer calculations?
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$K=\frac{1}{2}mv^2$. Kinetic energy depends on mass and velocity squared.
$K=\frac{1}{2}mv^2$. Kinetic energy depends on mass and velocity squared.
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What is the change in gravitational potential energy near Earth?
What is the change in gravitational potential energy near Earth?
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$\Delta U_g=mg\Delta h$. Gravitational PE change is weight times height change.
$\Delta U_g=mg\Delta h$. Gravitational PE change is weight times height change.
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What is the conservation of energy statement used in computational energy-transfer models?
What is the conservation of energy statement used in computational energy-transfer models?
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$E_{\text{in}}-E_{\text{out}}=\Delta E_{\text{system}}$. Energy conservation: input minus output equals system change.
$E_{\text{in}}-E_{\text{out}}=\Delta E_{\text{system}}$. Energy conservation: input minus output equals system change.
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What is the work done by a constant force parallel to the displacement?
What is the work done by a constant force parallel to the displacement?
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$W=Fd$. Work equals force times distance when parallel.
$W=Fd$. Work equals force times distance when parallel.
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What is the work done by a constant force at angle $\theta$ to the displacement?
What is the work done by a constant force at angle $\theta$ to the displacement?
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$W=Fd\cos\theta$. Cosine accounts for the component of force along displacement.
$W=Fd\cos\theta$. Cosine accounts for the component of force along displacement.
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What is the average power in terms of work done over a time interval?
What is the average power in terms of work done over a time interval?
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$P=\frac{W}{\Delta t}$. Power equals work divided by time interval.
$P=\frac{W}{\Delta t}$. Power equals work divided by time interval.
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What is the power definition used to model energy transfer rate?
What is the power definition used to model energy transfer rate?
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$P=\frac{\Delta E}{\Delta t}$. Power is energy transfer rate.
$P=\frac{\Delta E}{\Delta t}$. Power is energy transfer rate.
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What is the elastic potential energy stored in an ideal spring compressed or stretched by $x$?
What is the elastic potential energy stored in an ideal spring compressed or stretched by $x$?
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$U_s=\frac{1}{2}kx^2$. Spring PE is quadratic in displacement from equilibrium.
$U_s=\frac{1}{2}kx^2$. Spring PE is quadratic in displacement from equilibrium.
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Identify the computational update rule for energy using constant power over time step $\Delta t$.
Identify the computational update rule for energy using constant power over time step $\Delta t$.
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$E_{\text{new}}=E_{\text{old}}+P\Delta t$. Energy increases by power times elapsed time.
$E_{\text{new}}=E_{\text{old}}+P\Delta t$. Energy increases by power times elapsed time.
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What is the thermal energy transfer from kinetic friction over distance $d$ on a level surface?
What is the thermal energy transfer from kinetic friction over distance $d$ on a level surface?
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$E_{\text{th}}=f_k d=\mu_k N d$. Friction converts mechanical energy to thermal over distance.
$E_{\text{th}}=f_k d=\mu_k N d$. Friction converts mechanical energy to thermal over distance.
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What is the work formula for a constant force parallel to displacement?
What is the work formula for a constant force parallel to displacement?
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$W=Fd$. Work equals force times distance when force is parallel to motion.
$W=Fd$. Work equals force times distance when force is parallel to motion.
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What is the mechanical power relation connecting energy transfer and time?
What is the mechanical power relation connecting energy transfer and time?
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$P=\frac{\Delta E}{\Delta t}$. Power is the rate of energy transfer.
$P=\frac{\Delta E}{\Delta t}$. Power is the rate of energy transfer.
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What is the elastic potential energy formula for a spring in computational energy tracking?
What is the elastic potential energy formula for a spring in computational energy tracking?
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$U_s=\frac{1}{2}kx^2$. Elastic PE is proportional to spring constant and displacement squared.
$U_s=\frac{1}{2}kx^2$. Elastic PE is proportional to spring constant and displacement squared.
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What is the gravitational potential energy change near Earth used in energy models?
What is the gravitational potential energy change near Earth used in energy models?
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$\Delta U_g=mg\Delta h$. Gravitational PE change is weight times height change.
$\Delta U_g=mg\Delta h$. Gravitational PE change is weight times height change.
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What equation updates system energy when heat $Q$ is added and work $W$ is done by the system?
What equation updates system energy when heat $Q$ is added and work $W$ is done by the system?
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$\Delta E=Q-W$. First law of thermodynamics: energy change equals heat added minus work done by system.
$\Delta E=Q-W$. First law of thermodynamics: energy change equals heat added minus work done by system.
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What is the conservation of energy equation for a closed system in computational models?
What is the conservation of energy equation for a closed system in computational models?
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$E_{\text{initial}}=E_{\text{final}}$. Energy is conserved in closed systems with no external work or heat transfer.
$E_{\text{initial}}=E_{\text{final}}$. Energy is conserved in closed systems with no external work or heat transfer.
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What is the energy balance statement including nonconservative work $W_{\text{nc}}$?
What is the energy balance statement including nonconservative work $W_{\text{nc}}$?
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$\Delta K+\Delta U=W_{\text{nc}}$. Total mechanical energy change equals work done by nonconservative forces.
$\Delta K+\Delta U=W_{\text{nc}}$. Total mechanical energy change equals work done by nonconservative forces.
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Identify the correct discrete update for energy using constant power $P$ over time step $\Delta t$.
Identify the correct discrete update for energy using constant power $P$ over time step $\Delta t$.
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$E_{n+1}=E_n+P\Delta t$. Energy at next time step equals current energy plus power times time interval.
$E_{n+1}=E_n+P\Delta t$. Energy at next time step equals current energy plus power times time interval.
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Identify the correct discrete update for speed from kinetic energy $K$ and mass $m$.
Identify the correct discrete update for speed from kinetic energy $K$ and mass $m$.
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$v=\sqrt{\frac{2K}{m}}$. Rearranging $K=\frac{1}{2}mv^2$ to solve for velocity.
$v=\sqrt{\frac{2K}{m}}$. Rearranging $K=\frac{1}{2}mv^2$ to solve for velocity.
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Find $\Delta U_g$ for $m=1,\text{kg}$, $\Delta h=5,\text{m}$, $g=10,\text{m/s}^2$.
Find $\Delta U_g$ for $m=1,\text{kg}$, $\Delta h=5,\text{m}$, $g=10,\text{m/s}^2$.
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$50,\text{J}$. $\Delta U_g=(1)(10)(5)=50,\text{J}$.
$50,\text{J}$. $\Delta U_g=(1)(10)(5)=50,\text{J}$.
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