Chapter 9: Q. 23 (page 228)

A particle moving on the $x -$ axis experiences a force given by $F_{x} = q x^{2}$ , where $q$ is a constant. How much work is done on the particle as it moves from $x = 0$ to $x = d$ ?

Short Answer

Expert verified

Work done by particle $W_{0 \to d} = \frac{q d^{3}}{3}$

Step by step solution

Step 1. Given information

We have,

Force

F_{x} = q x^{3}

$q$ is constant

Step 2. Find the expression for the work done in the interval

A force F that acted on an object with mass m is parallel to the direction of motion and causes displacement delta rightarrowx for that object

$W = \int F_{x} d x$

We are given the force as a function of x by Fx=qx2

$W = \int F_{x} d x = \int_{0}^{d} q x^{2} d x = q \int_{0}^{d} x^{2} d x = q [\frac{1}{3} x^{3}]$

Now,

$W_{0 \to d} = q [\frac{1}{3} d^{3} - \frac{1}{3} {(0)}^{3}] = \frac{q d^{3}}{3}$

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A particle moving on the $x -$ axis experiences a force given by $F_{x} = q x^{2}$ , where $q$ is a constant. How much work is done on the particle as it moves from $x = 0$ to $x = d$ ?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the expression for the work done in the interval

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A particle moving on the x-axis experiences a force given by Fx=qx2 , where q is a constant. How much work is done on the particle as it moves from x=0 to x=d?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the expression for the work done in the interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Dynamics

Circular Motion and Gravitation

Thermodynamics

Nuclear Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

A particle moving on the $x -$ axis experiences a force given by $F_{x} = q x^{2}$ , where $q$ is a constant. How much work is done on the particle as it moves from $x = 0$ to $x = d$ ?