A rocket with a lift-off mass $20{,}000\ \text{kg}$ is blasted upwards with an initial acceleration of $5.0\ \text{m s}^{-2}$. Calculate the initial thrust (force) of the blast.

A rocket with a lift-off mass 20,000kg is blasted upwards with an initial acceleration of 5.0m s⁻². Calculate

Exercises · 4.9

20{,}000\ \text{kg}

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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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A rocket accelerating upward must overcome both gravity and provide net upward acceleration. Using Newton's second law with the total force as thrust minus weight, the initial thrust is $\boxed{2.96 \times 10^5 \text{ N}}$ .

When a rocket lifts off, two forces act on it: the upward thrust from the engines and the downward pull of gravity. The thrust must do double duty—it has to support the rocket's weight and accelerate it upward. This is why rockets need such enormous engines.

Newton's second law tells us that the net force equals mass times acceleration: $F_{\text{net}} = ma$ . The net force is what remains after all forces are accounted for. Here, that means thrust minus weight.

Identify the forces acting on the rocket.

The thrust $T$ acts upward (the force we want to find), and the weight $W = mg$ acts downward. Taking upward as positive, the net force is:

F_{\text{net}} = T - mg

Apply Newton's second law.

The rocket accelerates upward at $a = 5.0\ \text{m s}^{-2}$ , so:

F_{\text{net}} = ma

Combining with step 1:

T - mg = ma

Solve for the thrust $T$ .

Rearranging:

T = ma + mg = m(a + g)

This makes physical sense: the thrust must provide the acceleration $a$ plus counteract gravity $g$ .

Substitute the numerical values.

Given $m = 20{,}000\ \text{kg}$ , $a = 5.0\ \text{m s}^{-2}$ , and $g = 9.8\ \text{m s}^{-2}$ : …

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Q.A rocket with a lift-off mass $20{,}000\ \text{kg}$ is blasted upwards with an initial acceleration of $5.0\ \text{m s}^{-2}$ . Calculate the initial thrust (force) of the blast.

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

Concept: Newton's Second Law for a Rocket at Lift-off

Q.A rocket with a lift-off mass 20,000 kg20{,}000\ \text{kg}20,000 kg is blasted upwards with an initial acceleration of 5.0 m s−25.0\ \text{m s}^{-2}5.0 m s−2. Calculate the initial thrust (force) of the blast.

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Q.A rocket with a lift-off mass $20{,}000\ \text{kg}$ is blasted upwards with an initial acceleration of $5.0\ \text{m s}^{-2}$ . Calculate the initial thrust (force) of the blast.

Unlock everything free for 14 days