Question

The potential energy of a body of mass 2.5 kg is given by u= 3x-4y where x and y are the co ordinates of the body the acceleration of the body is

Answer 1

Answer:

force is negative gradient of a scalar ( potential energy) . so the answer will be 2 m/sec^2..

Answer 2

ACCELERATION IS 2 m/s².

Given:

• U = 3x - 4y
• Mass = 2.5 kg

To find:

Acceleration of the body ?

Calculation:

$U = 3x - 4y$

• Now , we will do partial derivative as follows:

$F_{x} = - \dfrac{ \partial U}{ \partial x}$

$\implies F_{x} = - \dfrac{ \partial (3x - 4y)}{ \partial x}$

$\implies F_{x} = -3 \: N$

Again, doing partial derivative:

$F_{y} = - \dfrac{ \partial U}{ \partial y}$

$\implies F_{y} = - \dfrac{ \partial (3x - 4y)}{ \partial y}$

$\implies F_{y} = 4 \: N$

So, net force will be :

$\implies F_{net} = \sqrt{ {( - 3)}^{2} + {4}^{2} }$

$\implies F_{net} = 5 \: N$

So, net acceleration is :

$\implies a = \dfrac{F_{net}}{mass}$

$\implies a = \dfrac{5}{2.5}$

$\implies a = 2 \: m {s}^{ - 2}$

So, acceleration is 2 m/s².