Q1. What is Newton’s 1st Law?

Background

Topic: Newton’s Laws of Motion

This question tests your understanding of Newton’s First Law, also known as the law of inertia, which describes the behavior of objects when no net force acts upon them.

Key Terms:

• Inertia: The tendency of an object to resist changes in its state of motion.

• Net Force: The vector sum of all forces acting on an object.

Step-by-Step Guidance

1. Recall that Newton’s First Law states that an object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by a net external force.

2. Think about examples: a book on a table stays at rest unless pushed; a hockey puck slides at constant speed on ice unless friction or another force acts.

3. Consider the implications: If the net force is zero, the velocity does not change (no acceleration).

Try explaining the law in your own words before checking the answer!

Q2. Determine the center of mass for the following system of particles:

Background

Topic: Center of Mass

This question tests your ability to calculate the center of mass for a system of particles using their masses and positions.

Key Formula:

• = mass of each particle

• = position of each particle

Step-by-Step Guidance

1. List the masses and positions of all particles in the system.

2. Multiply each mass by its corresponding position.

3. Add up all the mass-position products to get the numerator.

4. Add up all the masses to get the denominator.

5. Set up the formula for but stop before calculating the final value.

Try setting up the calculation before revealing the answer!

Q3. Which is an example of Newton’s 3rd Law?

Background

Topic: Newton’s Third Law of Motion

This question tests your understanding of action-reaction force pairs.

Key Terms:

• Action-Reaction Pair: For every action, there is an equal and opposite reaction.

Step-by-Step Guidance

1. Recall that Newton’s Third Law involves two objects exerting forces on each other.

2. Review each answer choice and ask: Does this describe two forces that are equal in magnitude and opposite in direction, acting on different objects?

3. Eliminate choices that do not fit the action-reaction pair definition.

Try identifying the correct example before checking the answer!

Q4. A box with a weight of 100 N is in motion. It is then pulled by a 30 N horizontal force. Is this enough force to keep it in motion?

Background

Topic: Forces and Friction

This question tests your understanding of the forces acting on an object, including friction and applied force, and how to determine if the applied force is sufficient to overcome friction.

Key Formulas:

• = friction force

• = coefficient of friction

• = normal force (equal to weight if horizontal)

Step-by-Step Guidance

1. Calculate the friction force using the weight of the box and the coefficient of friction (if given).

2. Compare the applied force (30 N) to the friction force.

3. If the applied force is greater than or equal to the friction force, the box will keep moving.

Try comparing the forces before revealing the answer!

Q5. Suppose you have a 2 kg mass on a spring. What is the spring constant if the spring stretches 10 cm under the weight?

Background

Topic: Hooke’s Law

This question tests your ability to use Hooke’s Law to relate the force exerted by a spring to its displacement and spring constant.

Key Formula:

• = force applied (equal to weight, )

• = spring constant

• = displacement (in meters)

Step-by-Step Guidance

1. Calculate the force due to the mass: .

2. Convert the displacement from centimeters to meters.

3. Set up Hooke’s Law: , but do not solve for yet.

Try setting up the equation before revealing the answer!

Q6. A block of mass m is accelerated across a rough surface by a force F at an angle φ above the horizontal. The frictional force is f. What is the horizontal acceleration of the block?

Background

Topic: Forces on an Inclined Plane

This question tests your ability to resolve forces into components and apply Newton’s Second Law in the horizontal direction.

Key Formulas:

• = applied force

• = angle above horizontal

• = friction force

• = mass

Step-by-Step Guidance

1. Resolve the applied force into horizontal and vertical components.

2. Write the sum of forces in the horizontal direction: .

3. Apply Newton’s Second Law: .

4. Set up the formula for but do not calculate the final value.

Try expressing the acceleration before revealing the answer!

Q7. Suppose you have a block sliding down a ramp at an angle θ. What is the acceleration if the coefficient of friction is μ?

Background

Topic: Inclined Planes and Friction

This question tests your ability to analyze forces on an inclined plane, including gravity and friction, and calculate acceleration.

Key Formula:

• = acceleration due to gravity

• = angle of incline

• = coefficient of friction

Step-by-Step Guidance

1. Resolve the gravitational force into components parallel and perpendicular to the ramp.

2. Calculate the friction force: .

3. Write the net force equation: .

4. Apply Newton’s Second Law: , and simplify to the formula above.

Try writing the acceleration formula before revealing the answer!

Q8. Using Newton’s Law of Gravitation, derive the acceleration due to Earth’s gravity “g”.

Background

Topic: Universal Gravitation

This question tests your ability to use Newton’s Law of Universal Gravitation to derive the formula for gravitational acceleration at Earth’s surface.

Key Formula:

• = universal gravitational constant

• = mass of Earth

• = radius of Earth

• = mass of object

Step-by-Step Guidance

1. Set the gravitational force equal to (Newton’s Second Law).

2. Cancel from both sides to solve for .

3. Substitute the values for , , and into the formula for .

4. Set up the calculation but do not compute the final value.

Try setting up the derivation before revealing the answer!

Q9. Solve for the orbital velocity of the Earth around the Sun.

Background

Topic: Circular Motion and Gravitation

This question tests your ability to relate gravitational force to centripetal force for an object in circular orbit.

Key Formulas:

• = mass of the Sun

• = mass of the Earth

• = distance between Sun and Earth

• = orbital velocity

Step-by-Step Guidance

1. Set the gravitational force equal to the centripetal force: .

2. Cancel from both sides and solve for .

3. Express in terms of , , and .

4. Set up the calculation but do not compute the final value.

Try expressing the velocity formula before revealing the answer!