8.2 Conservative and non-conservative forces  (Page 3/6)

What is the physical meaning of a non-conservative force?

A bottle rocket is shot straight up in the air with a speed $30\text{m/s}$ . If the air resistance is ignored, the bottle would go up to a height of approximately $46\text{m}$ . However, the rocket goes up to only $35\text{m}$ before returning to the ground. What happened? Explain, giving only a qualitative response.

An external force acts on a particle during a trip from one point to another and back to that same point. This particle is only effected by conservative forces. Does this particle’s kinetic energy and potential energy change as a result of this trip?

A force $F\left(x\right)=\left(3.0\text{/}x\right)\text{N}$ acts on a particle as it moves along the positive x -axis. (a) How much work does the force do on the particle as it moves from $x=2.0\text{m}$ to $x=5.0\text{m?}$ (b) Picking a convenient reference point of the potential energy to be zero at $x=\infty ,$ find the potential energy for this force.

A force $F\left(x\right)=\left(\mathrm{-5.0}{x}^2+7.0x\right)\text{N}$ acts on a particle. (a) How much work does the force do on the particle as it moves from $x=2.0\text{m}$ to $x=5.0\text{m?}$ (b) Picking a convenient reference point of the potential energy to be zero at $x=\infty ,$ find the potential energy for this force.

Find the force corresponding to the potential energy $U\left(x\right)=\text{−}a\text{/}x+b\text{/}{x}^2.$

The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by $U\left(x\right)=\text{−}a\text{/}{x}^{12}-b\text{/}{x}^6$ where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at $x=\infty )?$ (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?

A particle of mass $2.0\text{kg}$ moves under the influence of the force $F\left(x\right)=\left(3\text{/}\sqrt{x}\right)\text{N}.$ If its speed at $x=2.0\text{m}$ is $v=6.0\text{m/s,}$ what is its speed at $x=7.0\text{m?}$

A particle of mass $2.0\text{kg}$ moves under the influence of the force $F\left(x\right)=\left(\mathrm{-5}{x}^2+7x\right)\text{N}.$ If its speed at $x=\mathrm{-4.0}\text{m}$ is $v=20.0\text{m/s,}$ what is its speed at $x=4.0\text{m}?$

A crate on rollers is being pushed without frictional loss of energy across the floor of a freight car (see the following figure). The car is moving to the right with a constant speed $v_0.$ If the crate starts at rest relative to the freight car, then from the work-energy theorem, $Fd=m{v}^2\text{/}2,$ where d , the distance the crate moves, and v , the speed of the crate, are both measured relative to the freight car. (a) To an observer at rest beside the tracks, what distance $d\text{′}$ is the crate pushed when it moves the distance d in the car? (b) What are the crate’s initial and final speeds $v_0\text{′}$ and $v\text{′}$ as measured by the observer beside the tracks? (c) Show that $Fd\text{′}=m{\left(v\text{′}\right)}^2\text{/}2-m{\left(v{\text{′}}_0\right)}^2\text{/}2$ and, consequently, that work is equal to the change in kinetic energy in both reference systems.