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26 problems tagged with Incline
P0495
Advanced Mechanics › DynamicsBlock Sliding on a Stationary Wedge
A wedge of inclination angle $\theta$ and mass $m$ is placed on a horizontal table. An object, also of mass $m$, is placed on the inclined surface of the wedge. The coefficient of friction between the object and the wedge, and between the wedge and the table, is $\mu$.
- If the wedge is not to move backward as the object slides down, what relationship must $\mu$ and $\theta$ satisfy?
- If $\mu = 1/5$, what is the range of the angle $\theta$ that satisfies the above relationship?
P0497
Advanced Mechanics › DynamicsBlock on an Accelerating Inclined Plane
As shown in the figure, a block of mass $m$ is placed on the smooth inclined surface of a wedge. It is held in place by a thin string, with the other end of the string attached to a fixed backstop at the top of the wedge. Assume the angle of inclination is $\theta = 30^\circ$. The string will break when its tension reaches $2mg$. The entire system accelerates to the right with acceleration $a$.
P0406
Beginner Mechanics › DynamicsAcceleration of Blocks on an Incline
A block of mass $m_A$ on an inclined plane at angle $\theta$ is connected by a rope over a frictionless, massless pulley to a hanging block of mass $m_B$. The coefficients of static and kinetic friction between block A and the incline are $\mu_s$ and $\mu_k$. The positive direction is defined as up the incline, represented by the unit vector $\hat{i}$.
- In unit-vector notation, what is the acceleration of A if A is initially at rest?
- In unit-vector notation, what is the acceleration of A if A is initially moving up the incline?
- In unit-vector notation, what is the acceleration of A if A is initially moving down the incline?
P0407
Beginner Mechanics › DynamicsHanging Mass for Constant Velocity on Incline
Two blocks are connected over a frictionless, massless pulley as shown in the figure. The mass of block A is $m_A$. The coefficient of kinetic friction between block A and the incline is $\mu_k$. The angle of the incline is $\theta$. Block A slides down the incline at a constant speed. The connecting rope has negligible mass.
P0506
Advanced Mechanics › DynamicsBlock Sliding Down a Frictionless Movable Wedge
A wedge ABC of mass $M$ and height $h$ has an inclined surface AC with an angle $\theta$. A small object of mass $m$ is placed at the top A and slides down from rest. All contact surfaces are frictionless. Find:
- The displacement of $M$ when $m$ slides from the top to the bottom.
- The acceleration of $M$ relative to the ground, $a_1$, while $m$ is sliding.
- The acceleration of $m$ relative to $M$, $a'_2$.
- The acceleration of $m$ relative to the ground, $a_2$.
- The interaction force $N$ between $m$ and $M$.
- The normal force $R$ between $M$ and the table.
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.
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