MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4a Energy Conservation Mechanical Advantage

What this deck covers

This deck focuses on 4a Energy Conservation Mechanical Advantage, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

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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: What is the definition of mechanical energy $E_{mech}$ in terms of $K$ and $U$?

Answer: $E_{mech} = K + U$. Mechanical energy sums kinetic and potential energies, representing the total energy convertible between motion and position without losses.

Flashcard 2: Identify the input force needed to lift a load $F_{out}$ with an ideal machine having $MA = 4$.

Answer: $F_{in} = \frac{F_{out}}{4}$. For ideal machines, mechanical advantage inversely relates input and output forces, requiring one-fourth force to lift with MA=4.

Flashcard 3: State the formula for kinetic energy of a mass $m$ moving at speed $v$.

Answer: $K = \frac{1}{2}mv^2$. This equation calculates the energy of motion, arising from integrating force over distance for constant acceleration.

Flashcard 4: Find the compression $x$ of a spring that stops a mass $m$ moving at speed $v$ on a frictionless surface.

Answer: $x = v\sqrt{\frac{m}{k}}$. Equating initial kinetic energy to stored elastic potential gives the deformation where the spring constant balances mass and velocity.

Flashcard 5: Find the work done by kinetic friction over distance $d$ on a level surface with coefficient $\mu_k$.

Answer: $W_f = -\mu_k mgd$. Friction work is negative as it opposes motion, dissipating energy proportional to coefficient, weight, and distance on a flat surface.

Flashcard 6: What is the sign of work done by kinetic friction on a sliding object moving forward?

Answer: Negative work. Kinetic friction opposes motion, so the angle between force and displacement is 180°, yielding a negative cosine and energy dissipation.

Flashcard 7: State the formula for power in terms of work $W$ done over time interval $\Delta t$.

Answer: $P = \frac{W}{\Delta t}$. Power represents the rate of work done, averaging energy transfer over time for non-instantaneous processes.

Flashcard 8: State the magnitude of kinetic friction force in terms of $\mu_k$ and normal force $N$.

Answer: $f_k = \mu_k N$. Kinetic friction is proportional to the normal force, with $\mu_k$ as the coefficient depending on surface properties.

Flashcard 9: Identify the ideal MA for an ideal movable pulley with one pulley supporting the load by two rope segments.

Answer: $MA = 2$. The movable pulley halves the required input force by distributing the load across two rope segments ideally.

Flashcard 10: State the efficiency formula in terms of actual mechanical advantage (AMA) and IMA.

Answer: $\eta = \frac{AMA}{IMA}$. This relates actual performance (AMA) to theoretical maximum (IMA), highlighting losses in real machines.

Flashcard 11: Find the speed at the bottom after dropping from rest through height $h$ with no friction.

Answer: $v = \sqrt{2gh}$. Conservation of energy converts gravitational potential to kinetic, yielding speed independent of mass for free fall near Earth.

Flashcard 12: State the instantaneous power formula for a force $\vec{F}$ acting on a moving object with velocity $\vec{v}$.

Answer: $P = \vec{F}\cdot\vec{v}$. Instantaneous power is the dot product capturing the rate of energy transfer at a specific moment for varying forces or velocities.

Flashcard 13: State the formula for work done by a constant force $F$ over displacement $d$ at angle $\theta$.

Answer: $W = Fd\cos\theta$. Work measures energy transfer by force along displacement, with $\cos\theta$ accounting for the component parallel to motion.

Flashcard 14: Identify the energy conservation equation for a system including nonconservative work $W_{nc}$.

Answer: $K_i + U_i + W_{nc} = K_f + U_f$. This equation accounts for energy input or dissipation by nonconservative forces, balancing initial and final mechanical energies.

Flashcard 15: Identify the condition under which mechanical energy is conserved in a system.

Answer: Only conservative forces do work (no nonconservative work). Conservation holds when work is path-independent, as conservative forces like gravity store energy as potential without dissipation.

Flashcard 16: State the work–energy theorem relating net work $W_{net}$ to kinetic energy change.

Answer: $W_{net} = \Delta K$. The theorem states that net work on an object equals its change in kinetic energy, derived from Newton's second law integrated over displacement.

Flashcard 17: State the efficiency formula for a machine in terms of output and input work.

Answer: $\eta = \frac{W_{out}}{W_{in}}$. Efficiency quantifies the fraction of input work converted to useful output, less than 1 due to losses like friction.

Flashcard 18: Identify the ideal MA for an ideal fixed pulley (single pulley attached to the ceiling).

Answer: $MA = 1$. A fixed pulley changes force direction but not magnitude, resulting in no net force amplification ideally.

Flashcard 19: What is the definition of ideal mechanical advantage (IMA) using distances moved?

Answer: $IMA = \frac{d_{in}}{d_{out}}$. Ideal mechanical advantage assumes no energy losses, equating to the ratio of input to output distances based on geometry.

Flashcard 20: What is the ideal MA of an ideal block-and-tackle equal to, in terms of supporting rope segments $n$?

Answer: $MA = n$. In a block-and-tackle system, mechanical advantage equals the number of load-supporting ropes, amplifying force proportionally.

Flashcard 21: State the relationship between nonconservative work $W_{nc}$ and mechanical energy change $\Delta E_{mech}$.

Answer: $W_{nc} = \Delta E_{mech}$. Nonconservative forces like friction change mechanical energy through path-dependent work, equaling the net gain or loss in $E_{mech}$.

Flashcard 22: State the formula for gravitational potential energy near Earth for a mass at height $h$.

Answer: $U_g = mgh$. This formula quantifies the energy stored due to an object's position in a gravitational field, derived from the work done against gravity over height $h$.

Flashcard 23: What is the definition of mechanical advantage (MA) for a simple machine using forces?

Answer: $MA = \frac{F_{out}}{F_{in}}$. Mechanical advantage measures force amplification, defined as the ratio of output to input force in simple machines.

Flashcard 24: State the formula for elastic potential energy stored in an ideal spring compressed or stretched by $x$.

Answer: $U_s = \frac{1}{2}kx^2$. Elastic potential energy derives from Hooke's law, integrating force over displacement to store energy quadratically with deformation.

Flashcard 25: State the ideal simple-machine energy relation between input and output work.

Answer: $W_{in} = W_{out}$. In ideal machines without friction, energy conservation implies equal input and output work despite force-distance trade-offs.