Cards In This Deck

• $\text{You are given the mass }m\text{ and the acceleration vector }\mathbf{a}=x\mathbf{i}+y\mathbf{j}\text{. How do you calculate the magnitude of the force }|\mathbf{F}|\text{?}$
  $$\begin{gathered} \text{First find the force vector }\mathbf{F}=m\mathbf{a}\text{, then calculate the magnitude using Pythagoras.} \\ |\mathbf{F}|=|m(x\mathbf{i}+y\mathbf{j})|=m\sqrt{x^2+y^2} \end{gathered}$$
• $\text{Two particles connected by a slack string move apart. How do you find the common speed immediately after the string becomes taut?}$
  $\text{Apply Conservation of Momentum to the combined system of both particles.}$
• $$\begin{gathered} \text{True or False? } \\ \text{When Particle A collides with Particle B, the impulse exerted by A on B is larger if A is much heavier than B.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{By Newton’s 3rd Law, the impulses are equal in magnitude and opposite in direction (}{I}_{AB}=-I_{BA}\text{), regardless of mass.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{An object moving with constant velocity has no friction acting on it.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: Friction may still act, but the resultant force is zero.} \\ \text{Constant velocity means }a=0\text{, so Forward Force = Resistive Force (Friction).} \end{gathered}$$
• $\text{What is the formula for Weight (}W\text{) derived from SI base units?}$
  $$\begin{gathered} W=mg \\ \text{Where }m\text{ is mass (}kg\text{) and }g\text{ is acceleration due to gravity (}m{s}^{-2}\text{).} \end{gathered}$$
• $\text{What is the standard procedure for solving problems with a particle on an inclined plane?}$
  $$\begin{gathered} \text{1. Draw a large force diagram.} \\ \text{2. Define axes: Parallel to the slope (}//\text{) and Perpendicular to the slope (}\perp \text{).} \\ \text{3. Resolve all forces (specifically Weight }mg\text{) into these two components.} \\ \text{4. Apply }F=ma\text{ (parallel) and Equilibrium (perpendicular).} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{The normal reaction }R\text{ on an object of mass }m\text{ resting on an inclined plane is always equal to }mg\cos \alpha \text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }R=mg\cos \alpha \text{ only if there are no other external forces acting perpendicular to the plane.} \\ \text{If an external force }P\text{ pushes into the plane, }R=mg\cos \alpha +P\sin \theta \text{ (depending on angles).} \end{gathered}$$
• $\text{What is the mathematical consequence of modelling a string as inextensible?}$
  $\text{The magnitude of acceleration is the same for objects connected by the string.}$