2. Newtonian Dynamics

Dynamics Of Systems — Quiz

Test your understanding of dynamics of systems with 5 practice questions.

Practice Questions

Question 1

A uniform rope of mass $m$ and length $L$ hangs vertically. A constant upward force $F$ is applied to the top end of the rope. What is the tension $T(y)$ in the rope as a function of the distance $y$ from the bottom end, assuming the rope is accelerating upwards with acceleration $a$?

Question 2

A system consists of two blocks, $m_1$ and $m_2$, connected by a massless string over a frictionless pulley. Block $m_1$ is on a frictionless inclined plane at an angle $\theta$ with the horizontal, and block $m_2$ hangs vertically. If the system is released from rest and block $m_2$ moves downwards, what is the tension in the string?

Question 3

A rocket of initial mass $M_0$ (including fuel) is launched vertically. It expels fuel at a constant rate $R$ with an exhaust velocity $v_e$ relative to the rocket. Ignoring air resistance, what is the instantaneous acceleration of the rocket at time $t$?

Question 4

Consider a system where a block of mass $m$ is connected to a spring with spring constant $k$ on a frictionless horizontal surface. If the block is pulled a distance $x_0$ from its equilibrium position and released, what is the angular frequency of oscillation, $\omega$?

Question 5

A system consists of a cart of mass $M$ on a frictionless horizontal surface. Sand is added to the cart at a constant rate $\frac{dm}{dt} = R$. A constant external force $F_{ext}$ is applied to the cart. If the cart's velocity is $v$, what is the equation of motion for the cart?