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Chapter 7: Problem 7

If the difference in potential energy between two points is zero, does that necessarily mean that an object moving between those points experiences no force?

Short Answer

Expert verified
No, it doesn't necessarily mean that an object moving between those points experiences no force. Even if the difference in potential energy is zero, forces, especially non-conservative ones like friction, can still act on the object as the force is not path dependent and potential energy only evaluates the change in energy, not the forces acting.

Step by step solution

01

Understanding Potential Energy

Potential energy is the energy that an object has due to its position relative to other objects. It is dependent on the height and mass of the object and the gravitational field strength. It is given by the formula: \(PE = m.g.h\) where, PE = potential energy, m = mass, g = gravitational field strength, and h = height.
02

Understanding the relation between Force and Potential Energy

The force exerted on an object in a conservative field (like gravity, electrostatic field) is the negative gradient (rate of change) of that potential. So even if potential energy difference is zero, that doesn't necessarily mean that no force is being applied. It only indicates that the negation of the derivative of potential energy with respect to displacement (which gives the force) can be zero.
03

Example

For instance, if an object moves across a horizontal surface with no change in height, the gravitational potential energy change is zero. But if there is friction between the surfaces, there is a force acting on the object which doesn't change it's potential energy, but kinetic energy instead. In this scenario the work done by friction (a non-conservative force) isn't stored as potential energy, but dissipated as heat.

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Most popular questions from this chapter

The reservoir at Northfield Mountain Pumped Storage Project is \(214 \mathrm{m}\) above the pump/generators and holds \(2.1 \times 10^{10} \mathrm{kg}\) of water (see Application on p. 113 ). The generators can produce electrical energy at the rate of 1.08 GW. Find (a) the gravitational potential energy stored, taking zero potential energy at the generators, and (b) the length of time the station can generate power before the reservoir is drained.

In ionic solids such as \(\mathrm{NaCl}\) (salt), the potential energy of a pair of ions takes the form \(U=b / r^{n}-a / r,\) where \(r\) is the separation of the ions. For \(\mathrm{NaCl}, a\) and \(b\) have the SI values \(4.04 \times 10^{-28}\) and \(5.52 \times 10^{-98},\) respectively, and \(n=8.22 .\) Find the equilibrium separation in NaCl.

You fly from Boston's Logan Airport, at sea level, to Denver, altitude \(1.6 \mathrm{km} .\) Taking your mass as \(65 \mathrm{kg}\) and the zero of potential energy at Boston, what's the gravitational potential energy when you're (a) at the plane's 11 -km cruising altitude and (b) in Denver?

Your engineering department is asked to evaluate the performance of a new 370 -hp sports car. You know that \(27 \%\) of the engine's power can be converted to kinetic energy of the \(1200-\mathrm{kg}\) car, and that the power delivered is independent of the car's velocity. What do you report for the time it will take to accelerate from rest to 60 mi/h on a level road?

A particle slides back and forth on a frictionless track whose height as a function of horizontal position \(x\) is \(y=a x^{2},\) where \(a=0.92 \mathrm{m}^{-1} .\) If the particle's maximum speed is \(8.5 \mathrm{m} / \mathrm{s},\) find its turning points.
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