AP Physics 1 3.5: Power

LO 5.B.5.5, SP 2.2 2 points
Determine an expression for the mechanical power in terms of $M, H, \Delta t$, and physical constants, as appropriate.

For an expression that implies reasoning in terms of energy (as opposed to e.g., kinematics)

1 point

Example: M g H

For a correct expression for the power generated by the motor lifting the block at
constant speed

1 point

$M g H / \Delta t$

LO 5.B.9.2, SP 4.2, 6.4, 7.2; LO 5.B.9.3, SP 6.4, 7.2 5 points
Without M or H being changed, the time interval $\Delta t$ can be decreased by adding one resistor of resistance $R_{2}$, where $R_{2}>R_{1}$, to the circuit shown above. How should the resistor of resistance $R_{2}$ be added to the circuit to decrease $\Delta t$ ? In parallel with the battery In parallel with $R_{1}$ In parallel with the motor In series with the battery, $R_{1}$, and the motor

In a clear, coherent, paragraph-length response that may also contain figures and/or equations, justify why your selection would decrease $\Delta t$.

Correct answer: "In parallel with $R_{1}$ "

Note: If the wrong selection is made, the justification may still earn credit.

(b)

For a justification that correctly asserts that power must increase for $\Delta t$ to decrease, or
correctly asserting that the faster the rate of energy transfer means that works gets done
in a smaller time interval

1 point

For a correct assertion that current increases as resistance of the circuit decreases

Alternate Method: Potential difference across the parallel resistors will decrease if their resistance decreases.

1 point

For making the connection that there is an increase in current specifically in the motor because it is the same as the total current in the circuit

Alternate Method: There is an increase in potential difference specifically across the motor because the potential difference across the parallel resistors decreases (Kirchhoff's loop rule).

1 point

For a justification that indicates that connecting $R_{2}$ in parallel with $R_{1}$ will decrease the
equivalent resistance of the circuit

1 point

For a logical, relevant, and internally consistent argument that addresses the required argument or question asked, and follows the guidelines described in the published requirements for the paragraph-length response

1 point

Example Paragraph Response 1:

The work required to lift the block is M g H, so the rate at which the motor must do work to lift the block in the given time is $W / \Delta t=M g H / \Delta t$. The rate at which the motor does work increases with the potential difference across the motor (Note: This information is given in the question, so no points allotted in rubric for this statement.) To decrease the time, the motor must increase the rate at which the work is done, which requires a larger potential difference across the motor (or a larger current through the motor because $\Delta V=I R$ ). To increase the potential difference across the motor, the potential difference across $R_{1}$ must decrease, by Kirchhoff's loop rule (for a loop containing the battery, the motor and $R_{1}$ ). When $R_{2}$ is placed in parallel with $R_{1}$ the equivalent resistance of the combination decreases and the potential difference across that section decreases.

Example Paragraph Response 2:

Resistor $R_{2}$ should be connected in parallel with $R_{1}$. This will result in a smaller equivalent resistance in series with the battery and motor, so the current in the circuit (and through the motor) will be larger. The larger motor current results in the motor having a higher mechanical power. Because this power $M g H / \Delta t$ is larger and M g H is constant, the time interval $\Delta t$ will be smaller.

Learning Objectives

LO 5.B.5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance. [See Science Practices 2.2, 6.4]

LO 5.B.9.2: The student is able to apply conservation of energy concepts to the design of an experiment that will demonstrate the validity of Kirchhoff's loop rule $(\Sigma \Delta \mathrm{V}=0)$ in a circuit with only a battery and resistors either in series or in, at most, one pair of parallel branches. [See Science Practices 4.2, 6.4, 7.2]

LO 5.B.9.3: The student is able to apply conservation of energy (Kirchhoff's loop rule) in calculations involving the total electric potential difference for complete circuit loops with only a single battery and resistors in series and/or in, at most, one parallel branch. [See Science Practices 2.2, 6.4, 7.2]