Newton's Law

A block of mass $m$ is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude $F$ at an angle $\theta$ above the horizontal.

A chain consists of $N$ links, each of mass $m$. It is lifted vertically with a constant upward acceleration of magnitude $a$. The links are numbered 1 to $N$ from bottom to top. Let $g$ be the acceleration due to gravity.

A lamp of mass $m$ hangs from a cord in an elevator. The elevator experiences an upward acceleration of magnitude $a$, and the acceleration due to gravity is $g$.

An elevator cab of weight $W$ moves upward.

An elevator cab and its occupant have a combined mass $M$. The cab is pulled upward by a cable. When an occupant drops a coin, its downward acceleration relative to the cab is measured to be $a_{rel}$. The acceleration due to gravity is $g$.

A person and chair of combined mass $M$ are suspended by a massless rope over a massless, frictionless pulley. The system is to rise with an upward acceleration $a$. The rope's free end can be pulled either by the person in the chair or by a co-worker on the ground.

A particle moves with a constant velocity $\vec{v}$. Three forces, $\vec{F}_1$, $\vec{F}_2$, and $\vec{F}_3$, act on it. The first two forces are given by $\vec{F}_1 = F_{1x}\hat{i} + F_{1y}\hat{j} + F_{1z}\hat{k}$ and $\vec{F}_2 = F_{2x}\hat{i} + F_{2y}\hat{j} + F_{2z}\hat{k}$.

Two blocks, with masses $m_A$ and $m_B$, are on a frictionless horizontal surface. They are connected by a string of negligible mass. A force $\vec{F}_A$ acts on block A and a force $\vec{F}_B$ acts on block B. Both forces are directed along the positive x-axis.

Two forces with magnitudes $F_1$ and $F_2$ act on a body. The angle between the directions of the two forces is $\theta$. The resulting acceleration of the body has a magnitude of $a$.

A small ball is thrown vertically upwards. When it returns to the launching point, its speed is 3/4 of the initial speed. Assume the air resistance experienced by the ball during its motion is a constant force. Take $g = 10$ m/s².