Q1. Speed, Mass and Distance of Satellite

Background

Topic: Orbital Mechanics (Circular Motion and Gravity)

This question tests your understanding of how the speed of a satellite in a circular orbit depends on its mass and orbital radius.

Key Terms and Formulas

• Gravitational Force:

• Centripetal Force:

• For a satellite in circular orbit:

Step-by-Step Guidance

1. Write the equation for gravitational force providing the centripetal force for a satellite in circular orbit.

2. Notice that the mass of the satellite () appears on both sides of the equation.

3. Simplify the equation to solve for the orbital speed in terms of , , and .

4. Consider what happens to if the mass of the satellite changes, but and remain constant.

Try solving on your own before revealing the answer!

Q2. Displacement and velocity from Position vs Time

Background

Topic: Kinematics (Average Velocity)

This question asks you to calculate the average velocity over a specific time interval using a position vs. time graph or data.

Key Terms and Formulas

• Average velocity:

• = change in position, = change in time

Step-by-Step Guidance

1. Identify the position of the object at s and s from the graph or data.

2. Calculate the change in position: .

3. Calculate the change in time: .

4. Set up the formula for average velocity using your and values.

Try solving on your own before revealing the answer!

Q3. Acceleration from v-t Graph

Background

Topic: Kinematics (Graphs of Motion)

This question tests your understanding of how to determine acceleration from a velocity vs. time graph.

Key Terms and Formulas

• Acceleration:

• On a v-t graph, the slope represents acceleration.

Step-by-Step Guidance

1. Recall that the slope of a velocity vs. time graph gives the acceleration.

2. Consider what it means to find the slope: .

3. Think about what the area under the curve or reading the graph would represent instead.

Try solving on your own before revealing the answer!

Q4. a-t graph or F-t graph: Which best describes the motion if positive is East?

Background

Topic: Interpreting Acceleration-Time Graphs

This question asks you to interpret the motion of an object based on its acceleration-time graph, considering direction conventions.

Key Terms and Formulas

• Acceleration: The rate of change of velocity.

• Negative acceleration (when positive is East) means acceleration is toward the West.

Step-by-Step Guidance

1. Observe the graph: the acceleration is constant and negative (e.g., -2 m/s²).

2. Recall that negative acceleration (when positive is East) means the acceleration is directed West.

3. Consider the possible scenarios: Is the object moving East or West, and is it speeding up or slowing down?

4. Think about how negative acceleration affects an object moving East versus one moving West.

Try solving on your own before revealing the answer!

Q5. Solving Kinematic Problems: How long does it take to hit the ground? Which Equation is best?

Background

Topic: Kinematics (Free Fall)

This question tests your ability to select the appropriate kinematic equation for an object in free fall, given displacement and acceleration.

Key Terms and Formulas

• Displacement:

• Initial velocity:

• Acceleration: (usually m/s² for free fall)

• Kinematic equation:

Step-by-Step Guidance

1. Identify what is given: initial velocity, displacement, and acceleration.

2. Determine which kinematic equation relates these variables to time.

3. Set up the equation with the known values, leaving as the unknown.

Try solving on your own before revealing the answer!

Q6. Forces in Collision: Which exerts more force when they collide?

Background

Topic: Newton's Third Law (Action-Reaction)

This question tests your understanding of the forces two objects exert on each other during a collision.

Key Terms and Formulas

• Newton's Third Law: For every action, there is an equal and opposite reaction.

• Force during collision: Both objects exert equal and opposite forces on each other.

Step-by-Step Guidance

1. Recall Newton's Third Law and what it says about forces during interactions.

2. Consider whether the masses of the objects affect the magnitude of the force each exerts on the other during the collision.

3. Think about examples (e.g., a truck and a car colliding) and what happens to the forces involved.

Try solving on your own before revealing the answer!

Q7. Net force versus Velocity: A sailboat is being blown across the sea to the right at a constant velocity. What is the direction of the net force on the boat?

Background

Topic: Newton's First Law (Equilibrium)

This question tests your understanding of net force and motion at constant velocity.

Key Terms and Formulas

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

• Constant velocity: Implies zero acceleration and thus zero net force.

Step-by-Step Guidance

1. Recall Newton's First Law: An object moving at constant velocity has no net force acting on it.

2. Think about what it means for the forces acting on the boat (wind, water resistance, etc.).

3. Consider the direction of the net force if the velocity is not changing.

Try solving on your own before revealing the answer!

Q8. Recognizing Forces: The sketch shows possible forces acting on an object sliding downhill. Which choice shows the correct forces?

Background

Topic: Forces on an Inclined Plane

This question tests your ability to identify the correct forces acting on an object sliding down a slope.

Key Terms and Formulas

• Normal force: Perpendicular to the surface.

• Friction: Opposes motion, parallel to the surface.

• Weight: Acts vertically downward.

Step-by-Step Guidance

1. Recall the three main forces: gravity (weight), normal force, and friction.

2. Match each labeled force in the sketch to its correct physical force.

3. Eliminate choices that assign forces incorrectly (e.g., normal force not perpendicular, friction not parallel).

Try solving on your own before revealing the answer!

Q9. Breaking Vector into Components: What are the x and y components of F?

Background

Topic: Vectors and Components

This question tests your ability to resolve a vector into its x and y components using trigonometry.

Key Terms and Formulas

• Component form: ,

• Trigonometric relationships for right triangles.

Step-by-Step Guidance

1. Draw the vector at an angle from the x-axis.

2. Use the cosine function to find the x-component: .

3. Use the sine function to find the y-component: .

4. Check the sign of each component based on the direction of .

Try solving on your own before revealing the answer!

Q10. Example of Equilibrium Condition: A pendulum ball is at a position making an angle θ with the vertical. What forces are acting on the ball at this instant? Which equation best describes the equilibrium conditions along x and y directions?

Background

Topic: Equilibrium and Forces in Two Dimensions

This question tests your understanding of force components and equilibrium conditions for a pendulum at an angle.

Key Terms and Formulas

• Tension: (acts along the string)

• Weight: (acts vertically downward)

• Equilibrium: Net force in each direction is zero.

Step-by-Step Guidance

1. Draw a free-body diagram showing all forces acting on the pendulum ball.

2. Resolve the tension into x and y components: (horizontal), (vertical).

3. Write the equilibrium equations for the x and y directions, setting the net force to zero in each direction.

Try solving on your own before revealing the answer!

Q11. A 12 kg dog is having fun on a slide. The slide makes a 55° angle with the ground. If the coefficient of kinetic friction between the dog and slide is 0.45, what is the acceleration of the dog? Which equation describes the application of 2nd law of motion in x-direction?

Background

Topic: Newton's Second Law on an Inclined Plane with Friction

This question tests your ability to apply Newton's Second Law to an object sliding down an incline with friction.

Key Terms and Formulas

• Newton's Second Law:

• Forces along the incline: (down the incline), (friction, up the incline)

• Kinetic friction:

Step-by-Step Guidance

1. Draw a free-body diagram for the dog on the slide, showing all forces.

2. Write the expression for the net force along the incline: .

3. Express friction in terms of the normal force: .

4. Set up Newton's Second Law: .

Try solving on your own before revealing the answer!

Q12. Step 7: Writing the Equations. Value of the acceleration is...

Background

Topic: Centripetal Acceleration in Circular Motion

This question tests your ability to use the formula for centripetal acceleration in terms of velocity and radius, or angular velocity and radius.

Key Terms and Formulas

• Centripetal acceleration:

• Alternatively:

Step-by-Step Guidance

1. Identify the given quantities: velocity (), radius (), or angular velocity ().

2. Choose the appropriate formula for centripetal acceleration based on the given variables.

3. Set up the formula with the known values, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q13. Direction of Acceleration: A car drives through the bottom of a round valley while speeding up. What is the direction of the acceleration of the car when it is at the bottom of the valley at the position shown by the x?

Background

Topic: Circular Motion and Acceleration Vectors

This question tests your understanding of the direction of acceleration for an object in circular motion, especially when the speed is changing.

Key Terms and Formulas

• Centripetal acceleration: Always points toward the center of the circle.

• Tangential acceleration: Points in the direction of increasing speed.

• Total acceleration: Vector sum of centripetal and tangential accelerations.

Step-by-Step Guidance

1. Draw the velocity vectors just before and just after the car passes the bottom of the valley.

2. Determine the direction of the centripetal acceleration (toward the center of the circle, i.e., upward at the bottom).

3. Consider the tangential acceleration (in the direction of motion, since the car is speeding up).

4. Combine the two acceleration vectors to find the total acceleration direction at the bottom.

Try solving on your own before revealing the answer!

Q14. Turning on Banked Roads: Neglecting friction, which equation below describes motion along radial direction (r)?

Background

Topic: Circular Motion on Banked Curves

This question tests your understanding of the forces acting on a vehicle turning on a banked road without friction.

Key Terms and Formulas

• Normal force: (perpendicular to the surface)

• Radial (centripetal) direction: Points toward the center of the curve

• Centripetal force:

Step-by-Step Guidance

1. Draw a free-body diagram for the car on the banked curve, showing all forces.

2. Resolve the normal force into components: (vertical), (radial).

3. Set up the equation for the radial direction, equating the radial component of the normal force to the required centripetal force.

Try solving on your own before revealing the answer!

Q15. According to the law of gravity, what happens to the force when distance between two masses is reduced by half?

Background

Topic: Newton's Law of Universal Gravitation

This question tests your understanding of how gravitational force depends on the distance between two masses.

Key Terms and Formulas

• Gravitational force:

• If is reduced by half, changes by a factor of .

Step-by-Step Guidance

1. Write the formula for gravitational force between two masses.

2. Substitute for in the formula and simplify.

3. Compare the new force to the original force to see how it changes.

Try solving on your own before revealing the answer!