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Chapter 6: Problem 16

Can a potential energy function be defined for the force of friction?

Short Answer

Expert verified
Answer: No, a potential energy function cannot be defined for the force of friction, as it is a non-conservative force and its work done is path-dependent. Potential energy functions are only associated with conservative forces, where the work done depends solely on the initial and final positions, not on the path taken between them.

Step by step solution

01

Understand conservative forces and potential energy functions

A conservative force is a force that has a potential energy function associated with it. Mathematically, a force is conservative if its work done on an object moving around any closed path is zero. In other words, the work done depends only on the initial and final positions, and not on the path taken between the two points. Examples of conservative forces include gravitational force, spring force, and electrostatic force. For a conservative force, we can define a potential energy function, such that: 鈭� 脳 F = 0 Here, F is the force vector and 鈭� 脳 is the curl operator.
02

Examine the properties of friction

Friction is a contact force that opposes the relative motion between two surfaces in contact. The friction force can be either static or kinetic. The force of friction, F_f, is proportional to the normal force, N, acting on the object: F_f = 渭 * N Here, 渭 is the coefficient of friction. The work done by the force of friction is path-dependent and is generally different for different paths taken between two points.
03

Determine whether the force of friction is conservative

As the force of friction is path-dependent, the work done by friction around any closed path is not always zero. This means that the force of friction is a non-conservative force.
04

Answer the question: Can a potential energy function be defined for the force of friction?

Since the force of friction is a non-conservative force, a potential energy function cannot be defined for it. The potential energy functions are only associated with conservative forces, where the work done depends only on the initial and final positions and not on the particular path taken between these points.

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Most popular questions from this chapter

Which of the following is not a valid potential energy function for the spring force \(F=-k x ?\) a) \(\left(\frac{1}{2}\right) k x^{2}\) b) \(\left(\frac{1}{2}\right) k x^{2}+10 \mathrm{~J}\) c) \(\left(\frac{1}{2}\right) k x^{2}-10 \mathrm{~J}\) d) \(-\left(\frac{1}{2}\right) k x^{2}\) e) None of the above is valid.

A 20.0 -kg child is on a swing attached to ropes that are \(L=1.50 \mathrm{~m}\) long. Take the zero of the gravitational potential energy to be at the position of the child when the ropes are horizontal. a) Determine the child's gravitational potential energy when the child is at the lowest point of the circular trajectory. b) Determine the child's gravitational potential energy when the ropes make an angle of \(45.0^{\circ}\) relative to the vertical. c) Based on these results, which position has the higher potential energy?

A uniform chain of total mass \(m\) is laid out straight on a frictionless table and held stationary so that one-third of its length, \(L=1.00 \mathrm{~m},\) is hanging vertically over the edge of the table. The chain is then released. Determine the speed of the chain at the instant when only one-third of its length remains on the table.

A particle is moving along the \(x\) -axis subject to the potential energy function \(U(x)=1 / x+x^{2}+x-1\) a) Express the force felt by the particle as a function of \(x\). b) Plot this force and the potential energy function. c) Determine the net force on the particle at the coordinate \(x=2.00 \mathrm{~m}\)

A 1.00 -kg block is pushed up and down a rough plank of length \(L=2.00 \mathrm{~m},\) inclined at \(30.0^{\circ}\) above the horizontal. From the bottom, it is pushed a distance \(L / 2\) up the plank, then pushed back down a distance \(L / 4,\) and finally pushed back up the plank until it reaches the top end. If the coefficient of kinetic friction between the block and plank is \(0.300,\) determine the work done by the block against friction.
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