Newton's law of motion and its mathematical problems with solutions

Newton's First Law of Motion:

1. Problem: A car travels along a straight road at a constant speed of 20 m/s. What is the net force acting on the car?

   • Solution: Since the car moves at a constant speed, there is no change in velocity, and thus, according to Newton's first law, the net force acting on the car is zero.

2. Problem: A block rests on a frictionless surface. Determine the net force acting on the block.

   • Solution: The block is at rest, so its velocity is constant, and according to Newton's first law, the net force acting on the block is zero.

3. Problem: An object is moving with a velocity of 10 m/s to the right. What is the net force acting on the object?

   • Solution: If the object is moving with constant velocity, there is no acceleration, and according to Newton's first law, the net force acting on the object is zero.

4. Problem: A spacecraft is traveling through space with a constant velocity. Determine the net force acting on the spacecraft.

   • Solution: Since the spacecraft is traveling with constant velocity, there is no change in its motion, and according to Newton's first law, the net force acting on the spacecraft is zero.

5. Problem: A ball is rolling across a level surface without slowing down. Analyze the net force acting on the ball.

   • Solution: If the ball is rolling without any change in its motion, there is no net force acting on it according to Newton's first law.

Newton's Second Law of Motion:

6. Problem: A force of 50 N is applied to an object of mass 10 kg. Calculate the acceleration of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=50\text{N}$ and $𝑚=10\text{kg}$, we have $𝑎=\frac{𝐹}{𝑚}=\frac{50\text{N}}{10\text{kg}}=5{\text{m/s}}^2$.

7. Problem: If a force of 100 N is applied to an object of mass 5 kg, what is the resulting acceleration?

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=100\text{N}$ and $𝑚=5\text{kg}$, we have $𝑎=\frac{𝐹}{𝑚}=\frac{100\text{N}}{5\text{kg}}=20{\text{m/s}}^2$.

8. Problem: A 2 kg object experiences an acceleration of $6{\text{m/s}}^2$ under the influence of an unknown force. Determine the magnitude of the force.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=2\text{kg}$ and $𝑎=6{\text{m/s}}^2$, we have $𝐹=(2\text{kg})\times (6{\text{m/s}}^2)=12\text{N}$.

9. Problem: An object of mass 8 kg accelerates at $4{\text{m/s}}^2$ due to a force. Calculate the magnitude of the force.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=8\text{kg}$ and $𝑎=4{\text{m/s}}^2$, we have $𝐹=(8\text{kg})\times (4{\text{m/s}}^2)=32\text{N}$.

10. Problem: A force of 30 N is applied to an object, causing it to accelerate at $3{\text{m/s}}^2$. Determine the mass of the object.

    • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=30\text{N}$ and $𝑎=3{\text{m/s}}^2$, we rearrange the formula to find $𝑚$: $𝑚=\frac{𝐹}{𝑎}=\frac{30\text{N}}{3{\text{m/s}}^2}=10\text{kg}$.

Newton's Third Law of Motion:

11. Problem: A person pushes against a wall with a force of 200 N. What force does the wall exert on the person?

    • Solution: According to Newton's third law, the wall exerts an equal and opposite force on the person. So, the force exerted by the wall on the person is also 200 N but in the opposite direction.

12. Problem: A rocket engine exerts a force of 5000 N downward. What force does the rocket exert on the engine?

    • Solution: According to Newton's third law, the rocket exerts an equal and opposite force on the engine. So, the force exerted by the rocket on the engine is also 5000 N but upward.

13. Problem: A person jumps off a boat. If the person exerts a downward force of 800 N on the boat, what force does the boat exert on the person?

    • Solution: According to Newton's third law, the boat exerts an equal and opposite force on the person. So, the force exerted by the boat on the person is also 800 N but upward.

14. Problem: Two billiard balls collide. If ball A exerts a force of 50 N on ball B, what force does ball B exert on ball A?

    • Solution: According to Newton's third law, the force exerted by ball B on ball A is equal in magnitude (50 N) and opposite in direction to the force exerted by ball A on ball B.

15. Problem: A hammer strikes a nail with a force of 200 N. What force does the nail exert on the hammer?

    • Solution: According to Newton's third law, the force exerted by the nail on the hammer is equal in magnitude (200 N) and opposite in direction to the force exerted by the hammer on the nail.

16. Problem: A car crashes into a wall with a force of 3000 N. What force does the wall exert on the car?

    • Solution: According to Newton's third law, the wall exerts an equal and opposite force on the car. So, the force exerted by the wall on the car is also 3000 N but in the opposite direction to the car's motion.