AP Physics 1 2.5: Newton’s Second Law

LO 3.A.1.1, SP 1.5; LO 3.B.1.1, SP 6.4, 7.2

2 points
Suppose the mass of block A is much greater than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release.
Briefly explain your reasoning without deriving or using equations.

Examples of correct answers: "Zero", "small", "negligible", "much less than g", or
"<<g"

For a correct answer and attempt at a consistent justification

1 point

For correct reasoning

1 point

Example earning 1 point:
Nearly zero. Because block A is much heavier than block B.

Examples earning 2 points:
"Very small. Because block A has a large inertia, it won't speed up much."
"Close to zero because block B is so light that it can hardly budge block A."

Claim: The acceleration of the blocks is zero/small/negligible/ "<<g".
Evidence: The mass of block A is much greater than the mass of block B.
Reasoning: See two-point examples above.

1 point
Now suppose the mass of block A is much less than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release.
Briefly explain your reasoning without deriving or using equations.

ii.

Examples of correct answers: g or $9.8 \mathrm{~m} / \mathrm{s}^{2}$ or $10 \mathrm{~m} / \mathrm{s}^{2}$ (or just 9.8 or 10)

For a correct answer and correct justification

1 point

Examples:
Nearly equal to g. Because block B is almost in free fall.
$10 \mathrm{~m} / \mathrm{s}^{2}$, because block A has negligible mass and the tension in the string is nearly zero.

Claim: The acceleration of the blocks is close to g.
Evidence:
The mass of block A is much less than the mass of block B.
There is negligible friction between block A and the tabletop.
The pulley has negligible mass and spins with negligible friction about its axle.
Reasoning: See examples above.

LO 2.B.1.1, SP 2.2; LO 3.A.1.1, SP 1.5, 2.2; LO 3.B.1.3, SP 1.5, 2.2; LO 3.B.2.1, SP 1.4, 2.2; LO 4.A.2.1, SP 6.4 3 points

Derive an equation for the acceleration of the blocks after release in terms of $m_{A}, m_{B}$, and physical constants, as appropriate. If you need to draw anything other than what you have shown in part (b) to assist in your solution, use the space below. Do NOT add anything to the figure in part (b).

For using separate Newton's second law equations for each block

1 point

For combining the equations with correct notation, including correctly using $m_{A}$ and
$m_{B}$, indicating that the same tension force acts on both blocks, and that they share
the same acceleration

1 point

For a correct equation for a with supporting work: $a=\frac{m_{B}}{m_{A}+m_{B}} g$

1 point

Alternate Solution:

For writing a "whole-system" equation for the total mass that does not contain internal forces.
$$F_{\text {net }}=m_{\text {total }} a$$

1 point

For substituting the net force and system mass with correct quantities
$$m_{B} g=\left(m_{A}+m_{B}\right) a$$

1 point

Note: Writing the correct whole-system equation is sufficient to earn the first two points.

For a correct equation for a with supporting work: $a=\frac{m_{B}}{m_{A}+m_{B}} g$

1 point

LO 3.A.1.1, SP 2.2; LO 3.A.3.1, SP 6.4; LO 3.B.1.3, SP 2.2 1 point
Consider the scenario from part (a)(ii), where the mass of block A is much less than the mass of block B. Does your equation for the acceleration of the blocks from part (c) agree with your reasoning in part (a)(ii)? Yes No
Briefly explain your reasoning by addressing why, according to your equation, the acceleration becomes (or approaches) a certain value when $m_{A}$ is much less than $m_{B}$.

Correct answer: "Yes"

Note: "No" is acceptable if the equation is inconsistent with the answer in (a)(ii).

For valid reasoning that addresses the result in part (c) and the reasoning in part (a)(ii)

1 point

(d)

Claims:
Yes, the equation for the acceleration of the blocks from part (c) agrees with the reasoning in part (a)(ii).
or
No, the equation for the acceleration of the blocks from part (c) does not agree with the reasoning in part (a)(ii).

Evidence:
The mass of block A is much less than the mass of block B.

Reasoning for "Yes" claim:
When $m_{A}$ is much less than $m_{B}$, it can be neglected in the equation derived in part (c), giving an acceleration close to g as stated in (a)(ii).
Reasoning for "No" claim, if the answer in part (a)(ii) is wrong:
When $m_{A}$ is much less than $m_{B}$, it can be neglected in the equation derived in part (c), giving an acceleration close to g. This disagrees with the value of stated in (a)(ii).
Reasoning for "No" claim, if the answer in part (c) is wrong:
When $m_{A}$ is much less than $m_{B}$, it can be neglected in the equation derived in part (c), giving an acceleration of. This disagrees with the value of g stated in (a)(ii).