Newtons Second Law - Problems worksheet - Free Printable

Let's solve each problem step by step using Newton’s Second Law of Motion, which is:

> F = m × a
> Where:
> - F = Net force (in Newtons, N)
> - m = Mass (in kilograms, kg)
> - a = Acceleration (in meters per second squared, m/s²)

We'll also address the fill-in-the-blank questions at the end.

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1. How much force is needed to accelerate a 1000-kg car at a rate of 3 m/s²?

Given:
- m = 1000 kg
- a = 3 m/s²

Using:
F = m × a
F = 1000 × 3 = 3000 N

✔ Answer: 3000 N

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2. If a 70-kg swimmer pushes a pool wall with a force of 250 N, at what rate will the swimmer accelerate from the wall?

Given:
- F = 250 N
- m = 70 kg

Using:
a = F / m
a = 250 / 70 ≈ 3.57 m/s²

✔ Answer: 3.57 m/s²

(Rounded to 2 decimals as instructed)

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3. A weightlifter raises a 200-kg barbell with an acceleration of 3 m/s². How much force does the weightlifter use to raise the barbell?

Given:
- m = 200 kg
- a = 3 m/s²

F = m × a
F = 200 × 3 = 600 N

But wait — this assumes only upward acceleration. However, to lift the barbell, the weightlifter must overcome gravity and provide extra force for acceleration.

So total force = force to counteract gravity + force for acceleration

Gravity:
F_gravity = m × g = 200 × 9.8 = 1960 N

Force for acceleration:
F_accel = m × a = 200 × 3 = 600 N

Total force:
F_total = 1960 + 600 = 2560 N

✔ Answer: 2560 N

*(Note: The triangle diagram suggests F = m × a, but in real-world lifting, you must account for gravity unless otherwise stated. Since it says "raises" with acceleration, we assume net force includes overcoming gravity.)*

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4. A dancer lifts his partner above his head with an acceleration of 2.5 m/s². The dancer exerts a force of 200 N. What is the mass of the partner?

Given:
- F = 200 N
- a = 2.5 m/s²

Again, the force must overcome gravity and provide upward acceleration.

So:
Net force = F_applied = m × (g + a)
Because the total upward force must counteract gravity and produce acceleration.

So:
F = m × (g + a)
200 = m × (9.8 + 2.5)
200 = m × 12.3
m = 200 / 12.3 ≈ 16.26 kg

✔ Answer: 16.26 kg

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5. Newton’s second law of motion states that a(n) ________ force acting on an object causes it to accelerate according to the formula net force = mass × acceleration. Which means the acceleration of the object is directly proportional to the ________ and inversely proportional to the mass.

Fill in the blanks:

- First blank: unbalanced → because balanced forces result in no acceleration.
- Second blank: net force → acceleration is directly proportional to net force.

✔ Answer:
- unbalanced
- net force

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6. The two factors that affect acceleration are:

From Newton’s Second Law: F = m × a → so acceleration depends on:
- Net force
- Mass

So the correct answers are:
✔ force and mass

(Other options like speed, distance, weight are not direct factors in the formula.)

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7. Friction:

a. Is static friction when an object is not moving.
b. Is kinetic friction when two objects rub against each other.
i. Fluid friction – a special type of sliding friction when the object slides through a liquid or gas
c. Is rolling friction when the object rolls over another.

✔ Answers:
a. static friction
b. kinetic friction
i. fluid friction
c. rolling friction

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✔ Final Answers Summary:

1. 3000 N
2. 3.57 m/s²
3. 2560 N
4. 16.26 kg
5. unbalanced, net force
6. force, mass
7.
a. static friction
b. kinetic friction
i. fluid friction
c. rolling friction

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