Newton's Law

Inside a train moving on a straight, level track, an object of mass $m$ is suspended by a rope. When the train accelerates forward, the rope deflects towards the rear, making a constant angle $\theta$ with the vertical.

A car of mass $m_1$ pulls a trailer of mass $m_2$ along a horizontal road. The traction force on the car is $F$. The car and trailer experience resistance forces of $f_1$ and $f_2$, respectively.

Two iron blocks are placed in contact on a smooth horizontal table. Their masses are $M = 3$ kg and $m = 2$ kg. Two horizontal forces are applied to the blocks. Force $F = 15$ N is directed to the right, and force $f = 10$ N is directed to the left.

As shown in Figure, an object of mass $m$ is placed on an escalator. The object remains at rest relative to the escalator. The escalator moves upwards.

As shown in Figure, an object of mass $m$ is on a horizontal ground. It is pulled by a force of constant magnitude $F$ at an angle $\theta$ with the horizontal, causing it to move to the right. The coefficient of kinetic friction between the object and the ground is $\mu$.

On the floor of an elevator that is accelerating upwards at $a_e = 2 \text{ m/s}^2$, there is an inclined wedge A. The wedge has a length of 5 m and a height of 3 m. An object B with a mass of $m_B = 3$ kg is placed on the inclined surface of A. Both A and B are at rest relative to the elevator.

The resistance force on a moving train is 0.1 times its weight. Under the traction force of the locomotive, its forward acceleration is $a_1 = 1$ m/s². Due to some carriages detaching, while the traction force remains unchanged, the train's acceleration becomes $a_2 = 2$ m/s².

An object with a mass of $m=2$ kg is on a smooth horizontal plane, initially at rest. First, a force $F_1 = 6$ N is applied to it, directed east, for $t_1 = 2$ s. After 2 s, $F_1$ is removed, and immediately a force $F_2 = 8$ N, directed south, is applied for another $t_2 = 2$ s.

An object is thrown vertically upwards with a certain initial velocity. It experiences a constant air resistance force equal to 1/5 of its weight. The total time of flight, from launch until it returns to the starting point, is 6 s.

As shown in the diagram, a cart with mass $M$ is on a horizontal surface. On top of the cart, there is an object with mass $m_1$. A string connects $m_1$ to another object with mass $m_2$ which hangs over a pulley attached to the cart. The known masses are $M = 51$ kg, $m_1 = 5$ kg, and $m_2 = 4$ kg. The masses of the pulley, the supporting rod, and the inextensible string are negligible. All friction at contact surfaces is also ignored. A horizontal force $F$ is applied to the cart.