Unit 2: Force and Translational Dynamics
Weightage : 20-15%
Box \(A\) has a weight of \(5\,\mathrm{N}\) and is at rest on a horizontal floor. Box \(B\) has a weight of \(2\,\mathrm{N}\) and is at rest on top of box \(A\).
Which of the following free-body diagrams correctly represents the forces acting on the two boxes?
Correct Answer: \( \boxed{\mathrm{E}} \)
Since both boxes are at rest, each box is in static equilibrium, so the net force on each box is zero.
For box \(B\):
The forces are:
• Weight of \(2\,\mathrm{N}\) downward.
• Normal force from box \(A\) upward.
Therefore,
\(N_{A\rightarrow B}=2\,\mathrm{N}\).
For box \(A\):
The downward forces are its own weight \((5\,\mathrm{N})\) and the force exerted by box \(B\) \((2\,\mathrm{N})\). By Newton’s Third Law,
\(N_{B\rightarrow A}=N_{A\rightarrow B}=2\,\mathrm{N}\).
Thus, the floor must exert an upward normal force of
\(N_{\mathrm{floor}}=5+2=7\,\mathrm{N}\).
Diagram E correctly shows:
• Box \(B\): \(2\,\mathrm{N}\) upward normal and \(2\,\mathrm{N}\) downward weight.
• Box \(A\): \(7\,\mathrm{N}\) upward normal from the floor, \(5\,\mathrm{N}\) downward weight, and \(2\,\mathrm{N}\) downward force from box \(B\).
Therefore, the correct answer is (E).
In the tug-of-war shown above, person \(B\) pulls such that person \(A\) accelerates to the right while person \(B\) remains at rest.
Which of the following free-body diagrams provides evidence that Newton’s Third Law applies to this situation?
Correct Answer: \( \boxed{\mathrm{D}} \)
Newton’s Third Law states that if person \(A\) exerts a force on person \(B\), then person \(B\) exerts an equal-magnitude force in the opposite direction on person \(A\):
\(\vec{F}_{A\rightarrow B}=-\vec{F}_{B\rightarrow A}\).
Therefore, the tension force pulling person \(A\) to the right must be equal in magnitude to the tension force pulling person \(B\) to the left.
Person \(A\) accelerates to the right because the rightward tension force is greater than the leftward static friction acting on person \(A\).
Person \(B\) remains at rest because the leftward tension force is balanced by an equal rightward static friction force from the ground.
Diagram D correctly shows:
• Equal and opposite rope forces on the two people (Newton’s Third Law).
• An unbalanced net force to the right on person \(A\).
• Balanced horizontal forces on person \(B\), so person \(B\) remains at rest.
Therefore, the correct answer is (D).
Blocks \(A\) and \(B\) of masses \(1.0\,\mathrm{kg}\) and \(2.5\,\mathrm{kg}\), respectively, are on a horizontal surface and in contact with a circular vertical wall of radius \(1.25\,\mathrm{m}\). The blocks are also in contact with each other as shown in the top view. The horizontal surface has negligible friction, while the coefficient of kinetic friction between the vertical wall and the blocks is \(0.20\). A force of constant magnitude \(F\) is applied to block \(A\), always tangent to the circular wall, causing both blocks to move around the wall.
The top-view free-body diagrams below show the horizontal forces acting on each block. The frictional force from the wall is labeled \(f\), the normal force from the wall is labeled \(N\), the contact force between the blocks is labeled \(R\), and the applied force is labeled \(F\).
Which of the following provides evidence from the figures that supports Newton’s Third Law?
Correct Answer: \( \boxed{\mathrm{B}} \)
Newton’s Third Law states that whenever one object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction on the first object.
The force labeled \(R\) is the contact force between blocks \(A\) and \(B\). Therefore,
\(\vec{R}_{A\rightarrow B}=-\vec{R}_{B\rightarrow A}\).
In the free-body diagrams, the arrows representing \(R\) on the two blocks have the same length (equal magnitude) and point in opposite directions, exactly as required by Newton’s Third Law.
The other options either compare unrelated forces acting on the same object or describe forces that are not third-law pairs.
Therefore, the correct answer is (B).
