A position-dependent force F=x^2-3 Newton acts on a small body of mass 2 kg and displaces it fr

Name: Problem 29, Chapter 4: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T13:37:29-08:00
Duration: 1 min 32 s
Channel: Dheeraj Sharma
Description: A position-dependent force F=x^2-3 Newton acts on a small body of mass 2 kg and displaces it from x=0 to x=5 m. The work done is (A) 110 J (B) (80)/(3) J (D) (95)/(2) J (D) Zero

step 1 In this question we have given a position dependent force and we have to find the work done by t

Question

A position-dependent force $F=x^{2}-3$ Newton acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m}$. The work done is (A) $110 \mathrm{~J}$ (B) $\frac{80}{3} \mathrm{~J}$ (D) $\frac{95}{2} \mathrm{~J}$ (D) Zero

   A position-dependent force $F=x^{2}-3$ Newton acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m}$. The work done is
(A) $110 \mathrm{~J}$
(B) $\frac{80}{3} \mathrm{~J}$
(D) $\frac{95}{2} \mathrm{~J}$
(D) Zero

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 4, Problem 29

Instant Answer

Solved by Expert Dheeraj Sharma

10/06/2021

Step 1

The body of mass $2 \mathrm{~kg}$ is displaced from $x=0$ to $x=5 \mathrm{~m}$. We need to find the work done. Show more…

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A position-dependent force $F=x^{2}-3$ Newton acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m}$. The work done is (A) $110 \mathrm{~J}$ (B) $\frac{80}{3} \mathrm{~J}$ (D) $\frac{95}{2} \mathrm{~J}$ (D) Zero

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Key Concepts

Variable Force

This concept refers to a force whose magnitude or direction changes depending on the position of the object. When dealing with variable forces, simple multiplication of force and displacement is not sufficient, so calculus is required to calculate work done.

Work Done by a Force

Work is defined as the energy transferred by a force acting along a displacement. For variable forces, the work done is determined by integrating the force over the path of motion, which accounts for changes in force magnitude at different positions.

Definite Integral

A definite integral is a fundamental concept in calculus used to calculate the accumulation of quantities, such as work done, over a specific interval. It represents the area under the curve of a function between two limits, and in this context, it is used to sum the effect of a position-dependent force over a displacement.

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