MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

PE Diagram

The potential...

Question

The potential energy of an object of mass $m$ moving in $x y$ plane in a conservative field is given by $u = a x + b y$ , where $x$ and $y$ are position coordinates of the object. Find magnitude of its acceleration.

Open in App

Solution

Given
$U = a x + b y$

$F_{x} = - \frac{d U}{d x} = - a$

$F_{y} = - \frac{d U}{d y} = - b$

$m a_{x} = - a$

$a_{x} = - \frac{a}{m}$

and
$m a_{y} = - b$
$a_{y} = - \frac{b}{m}$

Net acceleration , $a = \sqrt{a_{x}^{2} + a_{y}^{2}} = \sqrt{(- \frac{a}{m})^{2} + (- \frac{b}{m})^{2}}$

Hence $a = \frac{\sqrt{a^{2} + b^{2}}}{m}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The potential energy of a body of mass

m

U = a x + b y

x

y

are position co-ordinates of the particle. The acceleration of the particle is

Q. A particle of mass

m

is moving in a field where the potential energy is given by

U (x) = U_{0} (1 - cos a x)

U_{0}

a

are positive constants and

x

is the displacement from mean position. Then (for small oscillations):

Q. The potential energy (in joule) of a body of mass

2 kg

x - y

plane is given by

U = 6 x + 8 y

, where the position coordinates

x

y

are measured in metres. The body is at rest at point

(6 m, 4 m)

t = 0

. It will cross the

y -

t

Q. The potential energy of a particle of mass 5 kg moving in x-y plane is given by equation,

U = - 7 x + 24 y

Joule.Here x and y are in meter at t=0,the particle is at origin and moving with velocity

(2^i + 3^j)

m/s.The magnitude of acceleration of particle is

Q. The potential energy (in joules) of a particle of mass

1 kg

moving in a plane is given by

U = 3 x + 4 y

. The position coordinates of the point being

x

y

, measured in metres. If the particle is at rest at

(6, 4)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Conservative Forces and Potential Energy

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon