Chapter 10: Interactions and Potential Energy

A system in which only one particle can move has the potential energy shown in $FIGUREEX10.30$. What is the x-component of the force on the particle at $x=5,15,$and $25cm$?

A system in which only one particle can move has the potential energy shown in $FIGUREEX10.31$. What is the y-component of the force on the particle at $y=0.5m$and $4m$?

A particle moving along the y-axis is in a system with potential energy $U=4y^{3}J$, where y is in m. What is the y-component of the force on the particle at $y=0m,1m,and2m$?

A particle moving along the x-axis is in a system with potential energy $U=10/xJ$, where x is in m. What is the x-component of the force on the particle at$x=2m,5m,and8m$?

$FIGUREEX10.34$shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force $F_x$as a function of position x.

A particle moves from A to D in $FIGUREEX10.35$while experiencing force$\overrightarrow{F}=(6\hat{i}+8\hat{j})N$. How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

A force does work on a $50g$particle as the particle moves along the following straight paths in the $xy$-plane: $25J$from $(0m,0m)$to $(5m,0m)$; $35J$from $(0m,0m)$to$(0m,5m)$; $–5J$from $(5m,0m)$to $(5m,5m)$; $–15J$from $(0m,5m)$to $(5m,5m)$; and $20J$from $(0m,0m)$to$(5m,5m)$.

a. Is this a conservative force?

b. If the zero of potential energy is at the origin, what is the potential energy at $(5m,5m)$?

A system loses$400J$ of potential energy. In the process, it does $400J$ of work on the environment and the thermal energy increases by $100J$. Show this process on an energy bar chart.

What is the final kinetic energy of the system for the process shown in $FIGUREEX10.38$?

How much work is done by the environment in the process shown in$FIGUREEX10.39$? Is energy transferred from the environment to the system or from the system to the environment?