A body of mass $5\ \text{kg}$ is acted upon by two perpendicular forces $8\ \text{N}$ and $6\ \text{N}$. Give the magnitude and direction of the acceleration of the body.

> [!TLDR] > The net force is the vector sum of the two perpendicular forces, giving a magnitude of $10\ \text{N}$ at an angle of $36.87^\circ$ from the $8\ \text{N}$ force. Using Newton's second law, the acceleration magnitude is $2\ \text{m/s}^2$ in the same direction. When two forces act on a body at right angles, the net effect is found by vector addition — the resultant is the diagonal of the rectangle they form. Newton's second law ($F = ma$) then converts that net force into acceleration. Perpendicular forces are independent, so we can treat the $x$ and $y$ components separately, then combine them. --- ### 1. Find the net force magnitude The two forces are perpendicular. Take: - $F_1 = 8\ \text{N}$ along the $x$-axis - $F_2 = 6\ \text{N}$ along the $y$-axis The magnitude of the resultant force $F_{\text{net}}$ is given by the Pythagorean theorem: $$F_{\text{net}} = \sqrt{F_1^2 + F_2^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\ \text{N}$$ > [!TIP] > The numbers 6, 8, 10 form a Pythagorean triple. Whenever you see perpendicular forces in a 3:4:5 ratio, the resultant is a clean number — a handy shortcut for exams. ### 2. Find the direction of the net force The direction is measured as the angle $\theta$ that $F_{\text{net}}$ makes with the $8\ \text{N}$ force (the $x$-axis): $$\tan \theta = \frac{F_2}{F_1} = \frac{6}{8} = 0.75 \implies \theta = \tan^{-1}(0.75) \approx 36.87^\circ$$ This angle is measured from the $8\ \text{N}$ force toward the $6\ \text{N}$ force. …

A body of mass 5kg is acted upon by two perpendicular forces 8N and 6N. Give the magnitude and direction of th

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Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.

The Intuition First

Two things matter when you push something:

How hard you push — the force you apply.
How heavy the object is — its mass.

The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.

Note

"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."

The Precise Statement

Newton's Second Law says:

The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.

In one equation:

\vec{a} = \frac{\vec{F}_{\text{net}}}{m}

Or more commonly:

\vec{F}_{\text{net}} = m \vec{a}

Where:

$\vec{F}_{\text{net}}$ is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
$m$ is the mass of the object — measured in kilograms (kg)
$\vec{a}$ is the acceleration — measured in metres per second squared ( $\text{m/s}^2$ )

\vec{F}_{\text{net}} = m \vec{a}

What This Really Means

Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).

Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.

Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.

A Simple Example

A 2 kg block is pushed with a net force of 10 N to the right.

a = \frac{F_{\text{net}}}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2

The block accelerates at $5\ \text{m/s}^2$ to the right. Every second, its velocity increases by 5 m/s in that direction. …

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The net force is the vector sum of the two perpendicular forces, giving a magnitude of $10\ \text{N}$ at an angle of $36.87^\circ$ from the $8\ \text{N}$ force. Using Newton's second law, the acceleration magnitude is $2\ \text{m/s}^2$ in the same direction.

When two forces act on a body at right angles, the net effect is found by vector addition — the resultant is the diagonal of the rectangle they form. Newton's second law ( $F = ma$ ) then converts that net force into acceleration.

Perpendicular forces are independent, so we can treat the $x$ and $y$ components separately, then combine them.

1. Find the net force magnitude

The two forces are perpendicular. Take:

$F_1 = 8\ \text{N}$ along the $x$ -axis
$F_2 = 6\ \text{N}$ along the $y$ -axis

The magnitude of the resultant force $F_{\text{net}}$ is given by the Pythagorean theorem:

F_{\text{net}} = \sqrt{F_1^2 + F_2^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\ \text{N}

Tip

The numbers 6, 8, 10 form a Pythagorean triple. Whenever you see perpendicular forces in a 3:4:5 ratio, the resultant is a clean number — a handy shortcut for exams.

2. Find the direction of the net force

The direction is measured as the angle $\theta$ that $F_{\text{net}}$ makes with the $8\ \text{N}$ force (the $x$ -axis):

\tan \theta = \frac{F_2}{F_1} = \frac{6}{8} = 0.75 \implies \theta = \tan^{-1}(0.75) \approx 36.87^\circ

This angle is measured from the $8\ \text{N}$ force toward the $6\ \text{N}$ force. …

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Q.A body of mass $5\ \text{kg}$ is acted upon by two perpendicular forces $8\ \text{N}$ and $6\ \text{N}$ . Give the magnitude and direction of the acceleration of the body.

Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

The Intuition First

The Precise Statement

What This Really Means

A Simple Example

1. Find the net force magnitude

2. Find the direction of the net force

Concept: Vector Addition of Perpendicular Forces, then Newton's Second Law

Q.A body of mass 5 kg5\ \text{kg}5 kg is acted upon by two perpendicular forces 8 N8\ \text{N}8 N and 6 N6\ \text{N}6 N. Give the magnitude and direction of the acceleration of the body.

1. Find the net force magnitude

2. Find the direction of the net force

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Q.A body of mass $5\ \text{kg}$ is acted upon by two perpendicular forces $8\ \text{N}$ and $6\ \text{N}$ . Give the magnitude and direction of the acceleration of the body.

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