Forces and Free-Body Diagrams AP Physics C Mechanics MCQ – Exam Style Questions etc.
Forces and Free-Body Diagrams AP Physics C Mechanics MCQ
Unit 2: Force and Translational Dynamics
Weightage : 20-15%
Question
A light, frictionless pulley is suspended from a rigid rod attached to the roof of an elevator car. Two masses, m and M ( with M > m), are suspended on either side of the pulley by a light, inextendable cord. The elevator car is descending at a constant velocity. Determine the acceleration of the masses.
(A) (M- m)g
(B) (M + m)g
(C) \(\frac{M+m}{M-m}g\)
(D) \(\frac{M-m}{M+m}g\)
(E) (M – m)(M + m)g\)
Answer/Explanation
Ans: D
Since the pulley is not accelerating, it can serve as the origin
of an inertial reference frame. Applying Newton’s Second
Law to the masses using the following free-body diagrams,
gives
\(F_T-mg= ma\) and \(Mg-F_T=Ma\)
Adding these equations eliminates \(F_T\) , and we find that
\(Mg – mg = (m +M) a \Rightarrow a = \frac{M – m}{M + m}g\)
The acceleration of block mis (M – m)g/(M + m) upward,
and the acceleration ofblockMis this value, (M – m)g/(M +
m), downward, which is (D).
Alternatively, you can treat the two objects as one system.
Tension is an internal force and cancels. The net force on the
system is Mg – mg. The total mass is M + m. If you simplify
this expression, you get the same answer, (D).
Answer/Explanation
Ans:D
This figure shows a vector pointing up and to the right. The component to the right is approximately equal to the vector to the left. The component upward is greater than the vector downward. This would indicate a net force and acceleration directed upward. Thus, if the brush is moving upward, it will be speeding up.
Question
A block of mass m is initially moving on a rough horizontal surface as shown in Figure 1. Figure 2 shows the four forces acting on the block. Which of the following best describes the motion of the block at the moment shown in the two figures?
A The block is moving to the right and speeding up.
B The block is moving to the right at a constant speed.
C The block is moving to the right and slowing down.
D The block is moving to the left at a constant speed.
E The block is moving to the left and slowing down.
Answer/Explanation
Ans:C
The velocity vector is to the right, indicating that the block is moving to the right. For the forces, the vector to the left is larger than the vector to the right, indicating that the net force and the resulting acceleration are to the left. An object moving to the right with an acceleration to the left is slowing down.Question
Blocks A and B of masses \(m_A\) and \(m_B\), respectively, are attached to an ideal pulley to create the Atwood’s machine shown in the figure. Which of the following free-body diagrams could be correct for the blocks when they are released from rest if \(m_B>m_A\)?
Answer/Explanation
Ans:D
Since block B has the greater mass, block B will accelerate downward, and block A will accelerate upward. The figure for block A shows a vector for its weight downward and a vector for the tension of the string upward. The tension is shown as greater than the weight; thus, the net force on block A is upward. The figure for block B shows a vector for its weight downward and a vector for the tension of the string upward. The weight is shown as greater than the tension; thus, the net force on block B is downward. Also, the tension on each block is correctly shown as having the same magnitude.