Embibe Experts Solutions for Exercise 3: Exercise 5.3

A simple pendulum consists of a $2.0 \mathrm{kg}$ mass attached to a string. It is released from rest at $x$ as shown. Its speed at the lowest point $y$ is

A block is released from rest at point $P$ and slides along the frictionless track shown. At point $Q,$ its speed is

A ball is held at a height $H$ above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy $E$ of the Earth-ball system as a function of the altitude $y$ of the ball?

The potential energy of a particle moving along the $x$-axis is given by $U\left(x\right)=8x^2+2x^4,$ where $U$ is in joules and $x$ is in meters. If the total mechanical energy is $9.0 \mathrm{J},$ the limits of motion are

The graphs below shows the force acting on a particle when it moves along the positive $x$-axis from the origin to $x=x_1.$ The force is parallel to the $x$-axis and is conservative. The maximum magnitude $F_1$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive)

A particle is released from rest at the point $x=a$ and moves along the $x$-axis subject to the potential energy function $U\left(x\right)$ shown. The particle

The diagram shows a plot of the potential energy as a function of $x$ for a particle moving along the $x$-axis. The points of stable equilibrium are

The first graph shows the potential energy $U\left(x\right)$ for a particle moving on the $x$-axis. Which of the following five graphs correctly gives the force $F$ exerted on the particle?