Physics

Problem

Two point masses are fixed on the

x

–

y

plane:

M_1=4\,\text{kg}

at the origin

(0,0)

and

M_2=6\,\text{kg}

(0.80\,\text{m},0)

. A point

P

has coordinates

(0.40\,\text{m},0.30\,\text{m})

. (i) Resolve and write the

x

- and

y

-components of the gravitational field strengths

\mathbf{E}_1

and

\mathbf{E}_2

produced at

P

M_1

and

M_2

respectively. (ii) Hence compute the components, magnitude, and direction (angle with the positive

x

-axis) of the net field at

P

. (iii) Discuss briefly how the result would change if

M_2

were moved farther away along the positive

x

-axis while all other data remained unchanged.

Intuitive explanation

The gravitational field is the force per unit mass that a point mass exerts on a test object—think of it as the "influence" a mass spreads through space. To find the total field at point $P$ , you need to calculate the field from each mass separately (using $E = GM/r^2$ and geometry to find components), then add them as vectors. The key is carefully working out the distance and direction from each mass to $P$ , then resolving each field into $x$ and $y$ parts before combining them.

Intuitive explanation

Browse the problem library