Browse Problems
37 problems tagged with Newton's Law in Dynamics
P0492
Advanced Mechanics › DynamicsVertical Throw with Constant Air Resistance
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.
- Find the ratio of the air resistance to the gravitational force.
- Find the ratio of the maximum height reached to the maximum height it would reach in a vacuum.
P0493
Advanced Mechanics › DynamicsInstantaneous Acceleration of Hanging Masses
As shown in the figure, three objects with masses $m_1$, $m_2$, and $m_3$ are hung in series and are initially at rest. Object 1 is attached above to an inextensible light string a. It is connected to object 2 by a light spring b, and object 2 is connected to object 3 by a light spring c. The springs are not necessarily identical.
- Find the acceleration of each object at the instant the string `a` is cut.
- Find the acceleration of the system's center of mass at that instant.
P0750
Expert Mechanics › DynamicsCar pulling objects through pulleys
A car and a heavy object D are connected by a rope passing over fixed pulleys B and C. Let $\phi$ be the angle between the vertical and the section of the rope connecting the car to pulley B.
The car starts from rest at point A, which is located directly below pulley B (where $\phi=0$), and moves with a constant acceleration $a=2m/s^2$. Given the weight of object D: $P=5kN$. Height of the pulleys $AB=3\sqrt{3}m$.
Initially, the rope is taut but has zero tension, and neglect the mass of the rope and pulleys, as well as the dimensions of the pulleys.
Find the tension in the rope when the angle $\phi=60^\circ$.
P0498
Advanced Mechanics › DynamicsShortest Sliding Time on an Elliptical Chord
As shown in the figure, for an ellipse with semi-major axis $a$ and semi-minor axis $b$, assume the major axis is vertical. A point mass of mass $m$ slides without friction under gravity along various straight chords passing through the center of the ellipse (referred to as "diameters").
P0508
Expert Mechanics › DynamicsInstantaneous Acceleration of a Pulley System
As shown in the figure, the masses of the three objects A, B, and C are $m_A = \frac{2\sqrt{3}}{3}m$, $m_B = 2m$, and $m_C = m$, respectively. Object C is connected to sliders A and B by two ropes that pass over two light, smooth pulleys, $O_1$ and $O_2$, at the same height. Sliders A and B are on fixed, smooth inclined planes with angles 60° and 30°, respectively. The system is initially in equilibrium. An object D with mass $m_D=m$ is gently hung on a hook below object C.
- Find the acceleration of object A at the instant D is hung.
- Find the acceleration of object B at the instant D is hung.
P0509
Expert Mechanics › DynamicsWedge and Blocks System Acceleration
As shown in the figure, a triangular wedge P of mass $M$ is placed between two blocks Q1 and Q2, of mass $m_1$ and $m_2$ respectively. The blocks can slide on a horizontal plane, and the system is released from rest. The angles between the sides of the wedge and the vertical are $\alpha$ and $\beta$. All surfaces are frictionless.
P0515
Expert Mechanics › DynamicsProjectile Motion with Linear Air Resistance
As shown in the figure, a small ball of mass $m$ is launched horizontally from point A with an initial velocity $v_0$. Under the influence of gravity and air resistance, it lands at point B. The velocity at B is $v'_0$, directed at an angle $\theta$ below the horizontal. The air resistance is given by the formula $f = -kv$, where $k$ is a positive constant and $v$ is the ball's velocity.
- Find the magnitude of the final velocity, $v'_0$.
- Find the horizontal distance between A and B, denoted by S.
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