The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=-7 x+24 y

Name: Problem 54, Chapter 6: Arihant AIEEE Physics
Uploaded: 2021-09-18T07:27:49-08:00
Duration: 1 min 17 s
Channel: Dharmendra Jain
Description: The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=-7 x+24 y joule, x and y being in metre. Initially at t=0 the particle is at the origin. (0,0) moving with a velocity of 6[2.4 î+0.7 ĵ] m / s. The magnitude of force on the particle is: (a) 25 units (b) 24 units (c) 7 units (d) none of these

step 1 This question we will learn about some basic concept of work energy and power, right? The questi

Question

The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x-y$ plane is given by $U=-7 x+24 y$ joule, $x$ and $y$ being in metre. Initially at $t=0$ the particle is at the origin. $(0,0)$ moving with a velocity of $6[2.4 \hat{\mathrm{i}}+0.7 \hat{\mathrm{j}}]$ $\mathrm{m} / \mathrm{s}$. The magnitude of force on the particle is: (a) 25 units (b) 24 units (c) 7 units (d) none of these

   The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x-y$ plane is given by $U=-7 x+24 y$ joule, $x$ and $y$ being in metre. Initially at $t=0$ the particle is at the origin. $(0,0)$ moving with a velocity of $6[2.4 \hat{\mathrm{i}}+0.7 \hat{\mathrm{j}}]$ $\mathrm{m} / \mathrm{s}$. The magnitude of force on the particle is:
(a) 25 units
(b) 24 units
(c) 7 units
(d) none of these

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 6, Problem 54

Instant Answer

Solved by Expert Dharmendra Jain

09/18/2021

Step 1

We know that the force vector is given by the negative gradient of the potential energy. Therefore, we can write the force as $\vec{F} = -\nabla U$. Show more…

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The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x-y$ plane is given by $U=-7 x+24 y$ joule, $x$ and $y$ being in metre. Initially at $t=0$ the particle is at the origin. $(0,0)$ moving with a velocity of $6[2.4 \hat{\mathrm{i}}+0.7 \hat{\mathrm{j}}]$ $\mathrm{m} / \mathrm{s}$. The magnitude of force on the particle is: (a) 25 units (b) 24 units (c) 7 units (d) none of these

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Key Concepts

Vector Magnitude Calculation

Once a force vector is determined, its magnitude is calculated using the Pythagorean theorem. This involves squaring each component of the force vector, summing these squares, and then taking the square root of the result. This method is essential in vector calculus to quantify the overall strength of a force irrespective of its direction.

Potential Energy and Force Relationship

In conservative systems, the force acting on a particle is derived from the potential energy function by taking the negative gradient. This means that each component of the force vector is found by taking the negative derivative of the potential energy with respect to the corresponding coordinate direction. This concept is central to connecting the scalar potential energy to the vector force field in mechanics.

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