Forces and Free-Body Diagrams AP Physics C Mechanics FRQ – Exam Style Questions etc.
Forces and Free-Body Diagrams AP Physics C Mechanics FRQ
Unit 2: Force and Translational Dynamics
Weightage : 20-15%
Question
Three blocks are connected by strings that pass over pulleys of negligible mass. Block B is on a level,mhorizontal surface of negligible friction. Block A is on top of block B. String 1 connects blocks A and B. The coefficients of static and kinetic friction between blocks A and B are \(\mu _s\) and \(\mu _k\), respectively. Block C is hanging over the end of the table and is attached to block B by string 2, as shown above. The masses of blocks A, B, and C are\( m_A\) , \(m_B\), and \(m_C\) , respectively. When block C is released, the system remains at rest.
(a)
i. On the dot below, which represents block A, draw and label the forces (not components) that act on block A. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
Block A
ii. On the dot below, which represents block B, draw and label the forces (not components) that act on block B. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
Block B
(b) Derive an expression for the maximum value for \(m_C\) at which the blocks will remain at rest. Express all algebraic answers in terms of \(\mu _s\), \(\mu _k\) , \(m_A \), \(m_B\),\( m_C\) , and physical constants, as appropriate.
The setup is modified, as shown in the figure above. Block A and one of the pulleys are removed, and block B remains on the table. There is still negligible friction between block B and the table. A lump of clay is added to block B. The students use Newton’s second law to derive an equation for the acceleration \(a_C\) of block C. The acceleration is given by the equation \(a_c=m_cg/m_{tot}\), where \(m_{tot} \)is the combined mass of the clay and the two blocks. Students use the setup shown above to experimentally determine the acceleration g due to gravity. In each trial, a student moves a small amount of clay from block B to block C and then releases the blocks from rest, recording the new values of \(m_C\) and \(a_C\). The total mass of the clay and the two blocks is \(m_{tot} \)5.0 kg tot . The graph below shows \(a_C\) as a function of \(m_C\), where \(m_C\) is now the combined mass of block C and the mass of clay added to block C.
(c)
i. Draw a best-fit line to the data points in the graph above.
ii. Use the best-fit line from part (c)(i) to calculate an experimental value for the acceleration g due to gravity.
(d) If the mass of the pulley in part (c) is significant, would the experimental value of g be greater than, less than, or equal to the value calculated in part (c)
(ii) ? ____ Greater than ____ Less than ____ Equal to Justify your answer.
A different group of students repeats the experiment, but instead of moving clay from block B to block C, they just remove a small amount of clay from block B and set it aside, away from the setup. The equation \(a_c=m_cg/m_{tot}\) still applies to the new experiment.
(e) In order to provide a straight-line graph that can be used to determine an experimental value for g, what two quantities should the students now graph? Check all that apply.
Justify your answer.
Answer/Explanation
(a)(i)
- For correctly drawing and labeling the vertical forces on block A
- For correctly drawing and labeling the horizontal forces on block A
Note: A maximum of one point can be earned if there are any extraneous vectors
(a) (ii)
- For correctly drawing and labeling the vertical forces on block B
- For correctly drawing and labeling the tension in string 1 to the left and the tension in string 2 to the right on block B
- For correctly drawing and labeling the static friction to the left on block B
Note: A maximum of two points can be earned if there are any extraneous vectors
(b) For an expression of Newton’s second law on block B
Expression of Newton’s second law on blocks A and C
For a correct expression for the frictional force
For an answer consistent with part (a)(ii) \(M_C=2\mu _{s}m_A\)
(c)
(i) For drawing an appropriate best-fit line
(c) (ii) For calculating the slope from the best-fit line and not from the data points unless the data points fall on the best-fit line
For correctly relating the slope to g
For calculating an experimental value for g with units
(d) Select “Less than”
For a correct justification
Example Justification: If the pulley has mass, the system will have more inertia and therefore the acceleration of the system be less. If the acceleration of the system is less, the experimental value of g is less. Note: “Greater than” is accepted if the student provides a reasonable justification.
(e) For selecting “\(a_{c}vs\frac{1}{m_{tot}}\) ” and “\(a_{c}vs\frac{m_c}{m_{tot}}\)”
For a correct justification
Example Justification: By removing the clay, the total mass is a variable. As the total mass of the system is decreased, the acceleration increase; thus\( a_c vs\frac{1}{m_{tot}} \)and \(a_{c}vs\frac{m_c}{m_{tot}}\)will generate a straight line graph that can be used to determine an experimental value for g.