Grade 8

Intermediate

10 min

Lesson 6 of 12

Applying F=ma

Not Started

Solving numerical problems to determine force, mass, or acceleration in various scenarios.

Ever wondered why a professional pitcher can throw a baseball at 100 mph, but would struggle to throw a heavy bowling ball even half that fast? It’s not just about strength—it’s the predictable math of the universe.

Learning Objectives

1.Calculate the required force to move a specific mass at a given acceleration.
2.Solve for acceleration when force and mass are known using algebraic rearrangement.
3.Predict how changing mass or force impacts the resulting motion of an object.

The Magic Formula: F = ma

Newton's Second Law of Motion tells us exactly how objects move when we push or pull them. The relationship is captured in one simple equation:

F = ma

. In this formula, Force (

F

) is measured in Newtons (

N

), Mass (

m

) is measured in kilograms (

kg

), and Acceleration (

a

) is measured in meters per second squared (

m/s^2

). One Newton is defined as the amount of force needed to accelerate

1 kg

of mass at a rate of

1 m/s^2

. Think of force as the 'effort,' mass as the 'heaviness,' and acceleration as the 'speed-up' result.

A student pushes an empty shopping cart with a mass of $15 kg$ . If they want the cart to accelerate at $2 m/s^2$ , how much force must they apply?

1. Identify the knowns: $m = 15 kg$ , $a = 2 m/s^2$ . 2. Use the formula: $F = m \times a$ . 3. Substitute the values: $F = 15 kg \times 2 m/s^2$ . 4. Solve: $F = 30 N$ .

Quick Check

If you double the force applied to an object but keep the mass the same, what happens to the acceleration?

Look at the formula

F = ma

. If

m

is constant, what happens to

a

when

F

goes up?

Answer

The acceleration will also double because force and acceleration are directly proportional.

Rearranging for Acceleration and Mass

We don't always look for force. Sometimes we know how hard we are pushing and want to find out how fast the object will speed up. By using basic algebra, we can rearrange the formula to solve for our missing variable. To find acceleration, we use

a = \frac{F}{m}

. To find mass, we use

m = \frac{F}{a}

. This shows us an inverse relationship: if you keep the force the same but increase the mass (make the object heavier), the acceleration will decrease. This is why a heavy truck takes longer to reach highway speeds than a light sports car.

A soccer player kicks a ball with a force of $12 N$ . The ball has a mass of $0.4 kg$ . What is the acceleration of the ball?

1. Identify the knowns: $F = 12 N$ , $m = 0.4 kg$ . 2. Choose the rearranged formula: $a = \frac{F}{m}$ . 3. Substitute the values: $a = \frac{12 N}{0.4 kg}$ . 4. Solve: $a = 30 m/s^2$ .

Quick Check

A mystery object is pushed with $10 N$ of force and accelerates at $5 m/s^2$ . What is its mass?

Use the formula

m = \frac{F}{a}

Answer

2 kg

The Impact of Friction and Net Force

In the real world, multiple forces often act on an object at once. The $F$ in $F=ma$ actually refers to the Net Force ( $F_{net}$ ). If you push a box with $10 N$ to the right, but friction pulls back with $2 N$ to the left, your net force is $10 N - 2 N = 8 N$ . You must use this resultant force in your calculations. If the forces are balanced (Net Force = 0), the acceleration is zero, meaning the object stays at a constant velocity or remains still.

Two dogs pull a $50 kg$ sled. Dog A pulls with $60 N$ and Dog B pulls with $40 N$ in the same direction. However, the snow creates a friction force of $20 N$ acting in the opposite direction. What is the sled's acceleration?

1. Calculate Net Force ( $F_{net}$ ): $(60 N + 40 N) - 20 N = 80 N$ . 2. Identify mass: $m = 50 kg$ . 3. Use the formula: $a = \frac{F_{net}}{m}$ . 4. Substitute: $a = \frac{80 N}{50 kg}$ . 5. Solve: $a = 1.6 m/s^2$ .

Key Takeaways

1The core formula is $F = ma$ , where force equals mass times acceleration.
2Force and acceleration are directly proportional; mass and acceleration are inversely proportional.
3Always ensure mass is in kilograms ( $kg$ ) and force is in Newtons ( $N$ ) before calculating.
4When multiple forces are present, calculate the Net Force ( $F_{net}$ ) before solving for $a$ or $m$ .

Quick Check

Multiple Choice

How much force is required to accelerate a $5 kg$ wagon at $3 m/s^2$ ?

Multiple Choice

If you apply $20 N$ of force to a $10 kg$ object, what is the acceleration?

True/False

If the mass of an object increases while the applied force stays the same, the acceleration will decrease.

What's Next?

Review Tomorrow

Tomorrow morning, try to write down the three variations of the $F=ma$ formula from memory and explain what 'Net Force' means.

Practice Activity

Find three items in your room (like a book, a shoe, and a chair). Estimate their mass in kg, and calculate how much force you would need to make each one accelerate at $9.8 m/s^2$ (the acceleration of gravity).

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Applying F=ma

Learning Objectives

The Magic Formula: F = ma

Rearranging for Acceleration and Mass

The Impact of Friction and Net Force

Key Takeaways

Quick Check

What's Next?

Applying F=ma

Learning Objectives

The Magic Formula: F = ma

Rearranging for Acceleration and Mass

The Impact of Friction and Net Force

Key Takeaways

Quick Check

What's Next?