Newton's laws and forces — Practice Quiz

A Physics cheat sheet for Newton's laws and forces — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Newton's Second Law: The net force \(\sum \vec{F}\) acting on an object is equal to the mass \(m\) of the object multiplied by its acceleration \(\vec{a}\).

$$\sum \vec{F} = m\vec{a}$$

Newton's Third Law: Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.

$$\vec{F}_{AB} = -\vec{F}_{BA}$$

Weight: The weight \(W\) of an object is the force of gravity acting on it, equal to its mass \(m\) times the acceleration due to gravity \(g\).

$$W = mg$$

Where: \(g\) = acceleration due to gravity (approx. \(9.8 m/s^2\) on Earth)

Newton's Law of Universal Gravitation: Every particle in the universe exerts an attractive force on every other particle.

$$F = G \frac{m_1 m_2}{r^2}$$

Where: \(G\) = universal gravitational constant, \(r\) = distance between centers

Maximum Static Friction: The maximum force of static friction \(f_s^{MAX}\) that can be exerted between two surfaces before sliding begins.

$$f_s^{MAX} = \mu_s F_N$$

Where: \(\mu_s\) = coefficient of static friction, \(F_N\) = normal force

Kinetic Friction: The force of kinetic friction \(f_k\) opposes the relative motion of two surfaces sliding past each other.

$$f_k = \mu_k F_N$$

Where: \(\mu_k\) = coefficient of kinetic friction

Equilibrium Conditions: For an object in equilibrium (at rest or constant velocity), the sum of forces in both x and y directions is zero.

$$\sum F_x = 0, \sum F_y = 0$$

Nonequilibrium Conditions (Newton's Second Law): When an object accelerates, the net force in each direction equals mass times the acceleration in that direction.

$$\sum F_x = ma_x, \sum F_y = ma_y$$

Practice quiz

  1. A $5 \text{ kg}$ object is subjected to a net force of $20 \text{ N}$. What is its acceleration?

    • $4 \text{ m/s}^2$
    • $0.25 \text{ m/s}^2$
    • $100 \text{ m/s}^2$
    • $25 \text{ m/s}^2$

    Answer: $4 \text{ m/s}^2$

  2. A book rests on a table. Which of the following is the Newton's Third Law action-reaction pair for the force of the Earth pulling down on the book?

    • The force of the table pushing up on the book.
    • The force of the book pushing down on the table.
    • The force of the book pulling up on the Earth.
    • The force of the Earth pulling down on the table.

    Answer: The force of the book pulling up on the Earth.

  3. An astronaut has a mass of $70 \text{ kg}$. What is her weight on Earth, where the acceleration due to gravity is approximately $9.8 \text{ m/s}^2$?

    • $70 \text{ N}$
    • $7.14 \text{ N}$
    • $686 \text{ N}$
    • $0.14 \text{ N}$

    Answer: $686 \text{ N}$

  4. According to Newton's Law of Universal Gravitation, if the distance between two masses is doubled, the gravitational force between them will:

    • Double.
    • Halve.
    • Quarter.
    • Quadruple.

    Answer: Quarter.

  5. A $10 \text{ kg}$ block rests on a horizontal surface. The coefficient of static friction between the block and the surface is $0.4$. What is the maximum static friction force that can be exerted on the block? (Assume $g = 9.8 \text{ m/s}^2$)

    • $39.2 \text{ N}$
    • $98 \text{ N}$
    • $4.0 \text{ N}$
    • $24.5 \text{ N}$

    Answer: $39.2 \text{ N}$

  6. A $5 \text{ kg}$ block is sliding across a horizontal surface with a coefficient of kinetic friction of $0.2$. What is the force of kinetic friction acting on the block? (Assume $g = 9.8 \text{ m/s}^2$)

    • $9.8 \text{ N}$
    • $19.6 \text{ N}$
    • $49 \text{ N}$
    • $0.2 \text{ N}$

    Answer: $9.8 \text{ N}$

  7. A $2 \text{ kg}$ object is suspended by a rope and is at rest. What is the tension in the rope? (Assume $g = 9.8 \text{ m/s}^2$)

    • $2 \text{ N}$
    • $19.6 \text{ N}$
    • $9.8 \text{ N}$
    • $0 \text{ N}$

    Answer: $19.6 \text{ N}$

  8. A $10 \text{ kg}$ box is pulled horizontally by a force of $50 \text{ N}$ across a frictionless floor. What is the acceleration of the box?

    • $0.2 \text{ m/s}^2$
    • $5 \text{ m/s}^2$
    • $500 \text{ m/s}^2$
    • $10 \text{ m/s}^2$

    Answer: $5 \text{ m/s}^2$

  9. A $3 \text{ kg}$ mass is attached to a string and is accelerating upwards at $2 \text{ m/s}^2$. What is the tension in the string? (Assume $g = 9.8 \text{ m/s}^2$)

    • $29.4 \text{ N}$
    • $6 \text{ N}$
    • $35.4 \text{ N}$
    • $23.4 \text{ N}$

    Answer: $35.4 \text{ N}$

  10. A $4 \text{ kg}$ block is pulled horizontally by a $20 \text{ N}$ force. If the coefficient of kinetic friction is $0.25$, what is the acceleration of the block? (Assume $g = 9.8 \text{ m/s}^2$)

    • $5 \text{ m/s}^2$
    • $2.55 \text{ m/s}^2$
    • $1.05 \text{ m/s}^2$
    • $0.5 \text{ m/s}^2$

    Answer: $2.55 \text{ m/s}^2$

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